Answer:
[tex]\displaystyle \frac{d}{dx} = \frac{3x - 5}{2x^\bigg{\frac{3}{2}}}[/tex]
General Formulas and Concepts:
Algebra I
Exponential Rule [Powering]: [tex]\displaystyle (b^m)^n = b^{m \cdot n}[/tex]Exponential Rule [Rewrite]: [tex]\displaystyle b^{-m} = \frac{1}{b^m}[/tex] Exponential Rule [Root Rewrite]: [tex]\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}[/tex]Calculus
Derivatives
Derivative Notation
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Derivative Rule [Quotient Rule]: [tex]\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \frac{3x + 5}{\sqrt{x}}[/tex]
Step 2: Differentiate
Rewrite [Exponential Rule - Root Rewrite]: [tex]\displaystyle \frac{3x + 5}{x^\bigg{\frac{1}{2}}}[/tex]Quotient Rule: [tex]\displaystyle \frac{d}{dx} = \frac{(x^\bigg{\frac{1}{2}})\frac{d}{dx}[3x + 5] - \frac{d}{dx}[x^\bigg{\frac{1}{2}}](3x + 5)}{(x^\bigg{\frac{1}{2}})^2}[/tex]Simplify [Exponential Rule - Powering]: [tex]\displaystyle \frac{d}{dx} = \frac{(x^\bigg{\frac{1}{2}})\frac{d}{dx}[3x + 5] - \frac{d}{dx}[x^\bigg{\frac{1}{2}}](3x + 5)}{x}[/tex]Basic Power Rule [Derivative Property - Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx} = \frac{(x^\bigg{\frac{1}{2}})(3x^{1 - 1} + 0) - (\frac{1}{2}x^\bigg{\frac{1}{2} - 1})(3x + 5)}{x}[/tex]Simplify: [tex]\displaystyle \frac{d}{dx} = \frac{3x^\bigg{\frac{1}{2}} - (\frac{1}{2}x^\bigg{\frac{-1}{2}})(3x + 5)}{x}[/tex]Rewrite [Exponential Rule - Rewrite]: [tex]\displaystyle \frac{d}{dx} = \frac{3x^\bigg{\frac{1}{2}} - (\frac{1}{2x^{\frac{1}{2}}})(3x + 5)}{x}[/tex]Rewrite [Exponential Rule - Root Rewrite]: [tex]\displaystyle \frac{d}{dx} = \frac{3\sqrt{x} - (\frac{1}{2\sqrt{x}})(3x + 5)}{x}[/tex]Simplify [Rationalize]: [tex]\displaystyle \frac{d}{dx} = \frac{3x - 5}{2x^\bigg{\frac{3}{2}}}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Derivatives
Book: College Calculus 10e
4/5×1 1/9÷2 2/3. please help me
Answer:
1/3
Step-by-step explanation:
when you change the mixed numbers to improper fractions, you get 4/5 * 10/9 ÷ 8/3. you can flip the 8/3 to 3/8 and change the division sign to multiplication, because dividing by a fraction is the same as multiplying by its reciprocal. you can cancel some things and ultimately you get 1/3
More math sorry. But I honestly don’t know any of these
Answer: A
Step-by-step explanation:
The main parent functions are x, and x raised to the power of something (examples: [tex]x^2, x^3, x^4[/tex], etc)
(URGENT!!) Which graph models the function f(x) = -4(2)x? (2 points)
Answer:
2nd Graph
Step-by-step explanation:
Bases off the graphs, you gave me, I assume your the equation is
[tex]f(x) = - 4(2) {}^{x} [/tex]
The parent equation of this function is
[tex]f(x) = b {}^{x} [/tex]
Let say x=0
Using the rules of exponets, the y value must be 1 so a critical point is
(0,1)
The function is multiplied by -4.
This means the function is stretched in the y direction by 4 and reflected over the x axis. So our new point will be
(0,-4).
The base 2 the function will get compressed by 1/2.
The best graph that represents this is the second graph
change the standard form equation into slope intercept form 13x-7y=23.
Which of the following is the value of a when the function (x) - 3|xlis written in the standard form of an absolute value
function?
Answer:1
Step-by-step explanation:2
2
The value of a when the function f(x) = 3|xl is written in the standard form of an absolute value function is 3.
What is meant by an absolute function ?An absolute function is defined as a function which consists of an algebraic expression that is within absolute value symbols.
Here,
The standard form of the absolute value function is written by,
f(x) = a|x|
Given that,
f(x) = 3|x|
Comparing this with the standard form, we get,
a|x| = 3|x|
Therefore, a = 3
Hence,
The value of a when the function f(x) = 3|xl is written in the standard form of an absolute value function is 3.
To learn more about absolute function, click:
https://brainly.com/question/14364803
#SPJ7
What is the probability of drawing 1 red marble out of a bag containing 4 red marbles, 3 green marbles, 2 blue marbles, and 1 purple marble?
Answer:
2/5
Step-by-step explanation:
There are a total of 4+3+2+1=10 marbles in the bag. Since there is an equal chance of drawing any marble from the bag, the chances of drawing a red marble is equal to the number of red marbles divided by the total number of marbles.
What we're given:
4 red marbles10 total marblesTherefore, the probability of drawing a red marble is:
[tex]\frac{4}{10}=\boxed{\frac{2}{5}}[/tex]
Answer: Most probably
Step-by-step explanation:
Gloria received a 4 percent raise and is now making $24,960 a year, what was her salary before the raise?
She gets a 4% raise so her new pay is 100% + 4% of her previous pay.
104% = 1.04 as a decimal.
Divide her new pay by 1.04:
24,960 / 1.04 = 24,000
Her previous pay was $24,000
Plz get me the correct answer or u will be reported. 15 points for correct answer. Thx.
Answer:
D
Step-by-step explanation:
correct answer, thanks for 15 pts
Answer:
Option D is correct
Step-by-step explanation:
Hope it is helpful....
In a race competition the probability that Harry wins is 0.4, the probability that Krish wins is 0.2 and the probability that Jonny wins is 0.3.
Find the probability that Harry and Jonny wins
Harry or Krish or Jonny wins
Someone else wins.
Answer:
jonny is the winner.
Step-by-step explanation:
No. of wins harry has = 0.4
No. of wins krish has = 0.2
No. of wins jonny has = 0.3
To find the prbability of harry and jonny = 0.4 + 0.3
= 0.7
Now to see who wins we have to add krish's wins and harry's win, because harry has the greatest number of wins.
krish = 0.2
harry = 0.4
= 0.6
now we have all three's score, so we will now see which is the greatest number.
krish= 0.6
harry = 0.4
jonny = 0.7
The greatest number is 0.7.
Hence, jonny is the winner!
HOPE IT HELPS PLZ MARK ME BRAINLIEST :D
Identify the sampling techniques used, and discuss potential sources of bias (if any). Assume the population of interest is the student body at a university. Questioning students as they leave an academic building, a researcher asks 341 students about their eating habits.
1. What type of sampling is used?
a. Systematic sampling is used, because students are selected from a list, with a fixed interval between students on the list.
b. Cluster sampling is used because students are divided into groups, groups are chosen at random, and every student in one of those groups is sampled.
c. Simple random sampling is used because students are chosen at random.
d. Stratified sampling is used because students are divided into groups, and students are chosen at random from these groups.
e. Convenience sampling is used because students are chosen due to convenience of location.
2. What potential sources of bias are present if any. Select all that apply.
a. University students may not be representative of all people in their age group.
b. The sample only consists of members of the population that are easy to get. These members may not be representative of the population.
c. Because of the personal nature of the question, students may not answer honestly.
d. There are no potential sources of bias.
Answer:
1. e. Convenience sampling is used because students are chosen due to convenience of location.
2. a. University students may not be representative of all people in their age group.
Step-by-step explanation:
Samples may be classified as:
Convenient: Sample drawn from a conveniently available pool.
Random: Basically, put all the options into a hat and drawn some of them.
Systematic: Every kth element is taken. For example, you want to survey something on the street, you interview every 5th person, for example.
Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.
Stratified: Also divides the population into groups. However, then only some elements of the group are surveyed.
Questioning students as they leave an academic building, a researcher asks 341 students about their eating habits.
Students sampled as they leave the build, which is convenience, in this case convenience of location, which means that the correct answer to question 1 is given by option e.
2. What potential sources of bias are present if any. Select all that apply.
Only members of one group are asked(university students), and this may not be representative of the rest of the population, which means that the correct answer to question 2 is given by option a.
In a pen of goats and chickens, there are 40 heads. and 130 feet How many goats and chickens are there?
Answer:
25 goat and 15 chicken
Step-by-step explanation:
Say the number of goats is G, then the number of chickens is 40 - G as there are 40 heads and each chicken and each goat has one head.
The number of feet is 130
So 2(40 - G) + 4G = 130
So 80 - 2G + 4G = 130
2G = 50
G = 25
25 goats and 15 chickens
4. One in four people in the US owns individual stocks. You randomly select 12 people and ask them if they own individual stocks. a. Find the mean, variance, and standard deviation of the resulting probability distribution. (3pts) b. Find the probability that the number of people who own individual stocks is exactly six. (3pts) c. Find probability that the number of people who say they own individual stocks is at least two. (3pts) d. Find the probability that the number of people who say they own individual stocks is at most two. (3pts) e. Are the events in part c. and in part d. mutually exclusive
Answer:
a. The mean is 3, the variance is 2.25 and the standard deviation is 1.5.
b. 0.0401 = 4.01% probability that the number of people who own individual stocks is exactly six.
c. 0.1584 = 15.84% probability that the number of people who say they own individual stocks is at least two.
d. 0.3907 = 39.07% probability that the number of people who say they own individual stocks is at most two
e. Both cases include one common outcome, that is, 2 people owning stocks, so the events are not mutually exclusive.
Step-by-step explanation:
For each person, there are only two possible outcomes. Either they own stocks, or they do not. The probability of a person owning stocks is independent of any other person, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
One in four people in the US owns individual stocks.
This means that [tex]p = \frac{1}{4} = 0.25[/tex]
You randomly select 12 people and ask them if they own individual stocks.
This means that [tex]n = 12[/tex]
a. Find the mean, variance, and standard deviation of the resulting probability distribution.
The mean of the binomial distribution is:
[tex]E(X) = np[/tex]
So
[tex]E(X) = 12(0.25) = 3[/tex]
The variance is:
[tex]V(X) = np(1-p)[/tex]
So
[tex]V(X) = 12(0.25)(0.75) = 2.25[/tex]
Standard deviation is the square root of the variance, so:
[tex]\sqrt{V(X)} = \sqrt{2.25} = 1.5[/tex]
The mean is 3, the variance is 2.25 and the standard deviation is 1.5.
b. Find the probability that the number of people who own individual stocks is exactly six.
This is P(X = 6). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 6) = C_{12,6}.(0.25)^{6}.(0.75)^{6} = 0.0401[/tex]
0.0401 = 4.01% probability that the number of people who own individual stocks is exactly six.
c. Find probability that the number of people who say they own individual stocks is at least two.
This is:
[tex]P(X \geq 2) = 1 - P(X < 2)[/tex]
In which
[tex]P(X < 2) = P(X = 0) + P(X = 1)[/tex]
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{12,0}.(0.25)^{0}.(0.75)^{12} = 0.0317[/tex]
[tex]P(X = 1) = C_{12,1}.(0.25)^{1}.(0.75)^{11} = 0.1267[/tex]
[tex]P(X < 2) = P(X = 0) + P(X = 1) = 0.0317 + 0.1267 = 0.1584[/tex]
0.1584 = 15.84% probability that the number of people who say they own individual stocks is at least two.
d. Find the probability that the number of people who say they own individual stocks is at most two.
This is:
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{12,0}.(0.25)^{0}.(0.75)^{12} = 0.0317[/tex]
[tex]P(X = 1) = C_{12,1}.(0.25)^{1}.(0.75)^{11} = 0.1267[/tex]
[tex]P(X = 2) = C_{12,2}.(0.25)^{2}.(0.75)^{10} = 0.2323[/tex]
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0317 + 0.1267 + 0.2323 = 0.3907[/tex]
0.3907 = 39.07% probability that the number of people who say they own individual stocks is at most two.
e. Are the events in part c. and in part d. mutually exclusive
Both cases include one common outcome, that is, 2 people owning stocks, so the events are not mutually exclusive.
work out the area of this shape ,give me right answer with explanation I’ll pay you
Answer:240 square centimeters
Step-by-step explanation:
1. 10x7=70
2. 7x10=70
3. 25x4=100
70+70+100=240
In a given region, the number of tornadoes in a one-week period is modeled by a Poisson distribution with mean 2. The numbers of tornadoes in different weeks are mutually independent. Calculate the probability that fewer than four tornadoes occur in a three-week period.
Answer:
0.1512 = 15.12% probability that fewer than four tornadoes occur in a three-week period.
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
In a given region, the number of tornadoes in a one-week period is modeled by a Poisson distribution with mean 2
Three weeks, so [tex]\mu = 2*3 = 6[/tex]
Calculate the probability that fewer than four tornadoes occur in a three-week period.
This is:
[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]
In which
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-6}*6^{0}}{(0)!} = 0.0025[/tex]
[tex]P(X = 1) = \frac{e^{-6}*6^{1}}{(1)!} = 0.0149[/tex]
[tex]P(X = 2) = \frac{e^{-6}*6^{2}}{(2)!} = 0.0446[/tex]
[tex]P(X = 3) = \frac{e^{-6}*6^{3}}{(3)!} = 0.0892[/tex]
Then
[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0025 + 0.0149 + 0.0446 + 0.0892 = 0.1512[/tex]
0.1512 = 15.12% probability that fewer than four tornadoes occur in a three-week period.
A rare baseball card just sold for $12,000. Sports experts anticipate this baseball card to increase in value by 9% each decade.
According to the experts, about how much should the baseball card be worth in 30 years?
Hint: A decade is equal to 10 years.
$15,540.35
$159,212.14
$83,614.45
$9042.85
Answer:
$15,540
Step-by-step explanation:
I DONT KNOW IF ITS RIGHT THO BUT
9% = 1,800
5. A cylindrical pipe is placed in a rectangular trench that is 5m x 4m
and 2.5m deep, is placed across the shorter side of the trench.
5.1 How much volume of cement will be needed to cover this hollow
pipe?
Answer:
The volume (density) of cement that will be needed to cover this hollow pipe is:
= 50,000 kg/m³
Step-by-step explanation:
Length of a cylindrical pipe = 5m
Width of the cylindrical pipe = 4m
Depth of the cylindrical pipe = 2.5m
The cubic meters of the cylindrical pipe = 5 * 4 * 2.5 = 50m³
1 cubic meter is equal to 1,000 kilogram
Therefore, the volume (density) of cement that will be needed to cover this hollow pipe is:
= 50 * 1,000
= 50,000 kg/m³
Can anyone help me with the question?
Answer:
-9
Step-by-step explanation:
(f-g) (x) = 2x²-7x+24-5x²-5x+3
= -3x²-12x+27
(f-g) (2) = -3(2)²-12(2)+27
= -12-24+27
= -9
What is the point estimate for the number of cars sold per week for a sample consisting of the following weeks: 1, 3, 5, 7, 10, 13, 14, 17, 19, 21?
A.
4.8
B.
5.22
C.
6.38
D.
6.1
Answer: A.
Step-by-step explanation:
Hope this helps!
when price of indomie noodles was lowered from #50 to #40 per unit, quantity demanded increases from 400 to 600 units per week. calculate the coefficient of price elasticity of demand and determine whether by lowering price this firm has made a wise decision
Answer:
The price elasticity of demand is -10
Step-by-step explanation:
Given
[tex]p_1,p_2 = 50,40[/tex]
[tex]q_1,q_2 = 400,500[/tex]
Solving (a): The coefficient of price elasticity of demand (k)
This is calculated as:
[tex]k = \frac{\triangle q}{\triangle p}[/tex]
So, we have:
[tex]k = \frac{500 - 400}{40 - 50}[/tex]
[tex]k = \frac{100}{-10}[/tex]
[tex]k = -10[/tex]
Because |k| > 0, then we can conclude that the company made a wise decision.
Х/10 is between 1/5
and 0.6. What could the value of x be?
Answer:
2 < x < 6
Step-by-step explanation:
x/10
1/5 = 2/10
.6 = 6/10
2 < x < 6
Moses receives a gift that is wrapped in a cube shaped box. The volume of the box is 1331/8 cubic inches.Find the length of a side of the box
Answer:
5.5inches
Step-by-step explanation:
1331/8=166.375
then length of a side is = cubic root of 166.375
=³√166.375
5.5
identify the system by type
Answer:
Inconsistent system
Step-by-step explanation:
Given
The attached graph
Required
The type of system
When two lines are parallel, it means they have the same slope and as such, the system has no solution.
Equations with the same slope are:
[tex]y = 2x + 6[/tex]
[tex]y = 2x- 8[/tex]
Both have a slope of 2
Such system are referred to inconsistent system.
Hence, (c) is correct.
What is the range of the table of values
Answer:
Range: { 0,3,5,7,9}
Step-by-step explanation:
The range is the values that y takes
Range: { 0,3,5,7,9}
Now we have to find,
The range of the table of values,
→ Range = ?
Then the range will be the numbers that is in the Y column.
→ Range = ?
→ Range = (value that Y takes)
→ Range = 0,3,5,7,9
Therefore, the range is 0,3,5,7,9.
2. Determine the number of all possible diagonals drawn for polygon having a. 7 sides b. 10 sides c. n - sides
Answer:
the number of diagonals can be found by n *n minus 3 by 2
a) the number of all possible diagonals drawn for having 7 side = 14 diagonals
b) the number of all possible diagonals drawn for having 10 side=35 diagonals
The polynomial 3x² + mx? - nx - 10 has a factor of (x - 1). When divided by x + 2, the remainder is 36. What are
the values of m and n?
Answer:
[tex]m = 12[/tex]
[tex]n =3[/tex]
Step-by-step explanation:
Given
[tex]P(x) = x^3 + mx^2 - nx - 10[/tex]
Required
The values of m and n
For x - 1;
we have:
[tex]x - 1 = 0[/tex]
[tex]x=1[/tex]
So:
[tex]P(1) = (1)^3 + m*(1)^2 - n*(1) - 10[/tex]
[tex]P(1) = 1 + m*1 - n*1 - 10[/tex]
[tex]P(1) = 1 + m - n - 10[/tex]
Collect like terms
[tex]P(1) = m - n + 1 - 10[/tex]
[tex]P(1) = m - n -9[/tex]
Because x - 1 divides the polynomial, then P(1) = 0;
So, we have:
[tex]m - n -9 = 0[/tex]
Add 9 to both sides
[tex]m - n = 9[/tex] --- (1)
For x + 2;
we have:
[tex]x + 2 = 0[/tex]
[tex]x = -2[/tex]
So:
[tex]P(-2) = (-2)^3 + m*(-2)^2 - n*(-2) - 10[/tex]
[tex]P(-2) = -8 + 4m + 2n - 10[/tex]
Collect like terms
[tex]P(-2) = 4m + 2n - 10 - 8[/tex]
[tex]P(-2) = 4m + 2n - 18[/tex]
x + 2 leaves a remainder of 36, means that P(-2) = 36;
So, we have:
[tex]4m + 2n - 18 = 36[/tex]
Collect like terms
[tex]4m + 2n = 36+18[/tex]
[tex]4m + 2n = 54[/tex]
Divide through by 2
[tex]2m + n=27[/tex] --- (2)
Add (1) and (2)
[tex]m + 2m - n + n = 9 +27[/tex]
[tex]3m =36[/tex]
Divide by 3
[tex]m = 12[/tex]
Substitute [tex]m = 12[/tex] in (1)
[tex]m - n =9[/tex]
Make n the subject
[tex]n = m - 9[/tex]
[tex]n = 12 - 9[/tex]
[tex]n =3[/tex]
The length of the box is 15 centimeters, the breadth of the box is 20 centimeter, the height of a box, 20 centimeter fine its volume. Step by step
Answer:
volume=length×width×height
v=15×20×20
v=6000
Which ordered pair is a solution of the equation?
y=-2x+5y=−2x+5y, equals, minus, 2, x, plus, 5
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
Only (2,-9)(2,−9)left parenthesis, 2, comma, minus, 9, right parenthesis
(Choice B)
B
Only (-2,9)(−2,9)left parenthesis, minus, 2, comma, 9, right parenthesis
(Choice C)
C
Both (2,-9)(2,−9)left parenthesis, 2, comma, minus, 9, right parenthesis and (-2,9)(−2,9)left parenthesis, minus, 2, comma, 9, right parenthesis
(Choice D)
D
Neither
9514 1404 393
Answer:
B. only (-2, 9)
Step-by-step explanation:
A graph of the equation makes it easy to see that (-2, 9) is a solution and (2, -9) is not.
You can try these values of x in the equation to see what the corresponding y-values are.
y = -2{-2, 2} +5 = {4, -4} +5 = {9, 1}
Points on the line are (-2, 9) and (2, 1).
(2, -9) is not a solution.
Answer:
B
Step-by-step explanation:
I know it is B. I know it because I put b in and I got it right on khan academy
I need help with this x/4 - 3x/8 = 5
Answer:
x=−40
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
x4−3x8=5
14x+−38x=5
(14x+−38x)=5(Combine Like Terms)
−18x=5
−18x=5
Step 2: Multiply both sides by 8/(-1).
(8−1)*(−18x)=(8−1)*(5)
x=−40
Answer:
x=−40
Hello!
x/4 - 3x/8 = 5
2x - 3x = 40
-x = 40
x = -40
Good luck! :)
PLEASE ANYONE definition of a percent increase?
Answer:
In any quantitative science, the terms relative change and relative difference are used to compare two quantities while taking into account the "sizes" of the things being compared. The comparison is expressed as a ratio and is a unitless number.
Step-by-step explanation:
I hope it helps
A radioactive material is known to decay at a yearly rate proportional to the amount at each moment. There were 1000 grams of the material 10 years ago. There are 980 prams right now. What will be the amount of the material right after 20 years?
a. 10 ln 2/ln(1000/980)
b. 10^6/980
c. 980^3/10^6
d. 980^2/10^3
Answer:
Amount left is 941.95 g.
Step-by-step explanation:
initial amount = 1000 g
time = 10 years
amount left = 980 grams
Now
[tex]980 = 1000 e^{-\lambda t}\\\\e^{\lambda\times 10}= 1.02\\\\10 \lambda = ln 1.02\\\\\lambda = 1.98\times10^{-3} per year[/tex]
time t = 20 years
Let the amount is N.
[tex]980 = 1000 e^{-\lambda t}\\\\e^{\lambda\times 10}= 1.02\\\\10 \lambda = ln 1.02\\\\\lambda = 1.98\times10^{-3} per year\\N = 980 e^{- 1.98\times 10^{-3}\times 20}\\\\ln N = ln 980 - 0.0396\\\\ln N = 6.88 - 0.0396 = 6.86\\\\N = 941.95 g[/tex]