After a shipwreck, 120 rats manage to swim from the wreckage to a deserted island. The population on the island grows exponentially according to the model n(t)-ne", where n(t)is the number of rats at time t in months. After 15 months there are 280 rats on the island a. Find a function that models the population t months after the arrival of the rats. b. What will the population be 3 years after the shipwreck? Round to a whole number. c. When will the population reach 2000 rats?
Answers
Complete Question
The complete question is shown on the first uploaded image
Answer:
a
[tex]n(t) = 120 e^{(0.056t)}[/tex]
b
[tex]n(36) = 901 \ rats[/tex]
c
[tex]t = 50 \ months[/tex]
Step-by-step explanation:
From the question we are told that
The original number of rats that swim from the wreckage to a deserted island is
The population on the island grows exponentially according to the model
[tex]n(t) = n_o e^{rt}[/tex]
The number of rats after t = 15 months is 280
So
[tex]n(15) = 120 e^{15 * r } = 280[/tex]
=> [tex]120 e^{15 * r } = 280[/tex]
=> [tex]e^{15r} = 2.33[/tex]
=> [tex]15r = 0.8459[/tex]
=> [tex]r = 0.056[/tex]
Therefore the population t months after the arrival of the rats is mathematically represented as
[tex]n(t) = 120 e^{(0.056t)}[/tex]
Here t is in months
Considering question b
For t = 3 years = 12 * 3 = 36 months
Then the number of rats that will be present is mathematically represented as
[tex]n(36) = 120 e^{0.056 * 36 }[/tex]
[tex]n(36) = 901 \ rats[/tex]
Considering question c
Now the number of rats considered is n(t) = 2000
So
[tex]n(t) = 2000 = 120e^{0.056t}[/tex]
=> [tex]2000 = 120e^{0.056t}[/tex]
=> [tex]16.67 = e^{0.056t}[/tex]
Taking natural log of both sides
=> [tex]0.056 t = 2.81[/tex]
=> [tex]t = 50 \ months[/tex]
Related Questions
to find the distance between (17,3) and (17,-5), marcia used the following equation. is marcia correct
Answers
Answer:
Distance = 8
[tex]Formula =\\\sqrt{(x_2-x_1)^2+(y_2-y_2)^2}[/tex]
Step-by-step explanation:
[tex](17,3)=(x_1 , y_1 )\\ (17,-5)=(x_2,y_2)\\\\d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\\\d = \sqrt{(17-17)^2+(-5-3)^2}\\\\ d = \sqrt{(0 )^2+(-8)^2}\\\\d = \sqrt{0 +64}\\\\ d = \sqrt{64} \\\\d = 8[/tex]
log 5 +3 log 2-log4÷log10
Answers
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Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
Let's simplify step-by-step.
[tex]Log (5) + (3 log (2)) - \frac{log(4)}{log(10)}[/tex]
[tex]= 0.69897 + 3(log (2)) - \frac{log (4)}{log (10)}[/tex]
[tex]= 0.69897 + (3) (0.30103) - \frac{log (4)}{log(10)}[/tex]
[tex]= 0.69897 + 0.90309 - \frac{log (4)}{log(10)}[/tex]
[tex]= 1.60206 - \frac{log(4)}{log(10)}[/tex]
[tex]= 1.60206 - \frac{1.60206}{log (10)}[/tex]
[tex]= 1.60206 - \frac{1.60206}{1}[/tex]
[tex]= 1.60206 - 0.60206[/tex]
[tex]= 1[/tex]
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Have a great day/night!
❀*May*❀
24 - 4 x 2 + 4b = 20 - 16
Answers
Answer:
b = -3
Step-by-step explanation:
Solve for b:
4 b - 4 2 + 24 = 20 - 16
-4×2 = -8:
4 b + -8 + 24 = 20 - 16
Grouping like terms, 4 b - 8 + 24 = 4 b + (24 - 8):
4 b + (24 - 8) = 20 - 16
24 - 8 = 16:
4 b + 16 = 20 - 16
20 - 16 = 4:
4 b + 16 = 4
Subtract 16 from both sides:
4 b + (16 - 16) = 4 - 16
16 - 16 = 0:
4 b = 4 - 16
4 - 16 = -12:
4 b = -12
Divide both sides of 4 b = -12 by 4:
(4 b)/4 = (-12)/4
4/4 = 1:
b = (-12)/4
The gcd of -12 and 4 is 4, so (-12)/4 = (4 (-3))/(4×1) = 4/4×-3 = -3:
Answer: b = -3
How to find solutions to Discriminat
Answers
Answer:
The discriminant is the expression b2 - 4ac, which is defined for any quadratic equation ax2 + bx + c = 0. Based upon the sign of the expression, you can determine how many real number solutions the quadratic equation has. If you get a positive number, the quadratic will have two unique solutions
Step-by-step explanation:
hope it help
Answer:
D = b² - 4ac
Step-by-step explanation:
if,
ax² + bx + c = 0
Select all of the expressions that are not equivalent to ax+bx+ac+bc. A.) x(a+b)+c(a+b) B.) a(x+c)+b(x+c) C.) (b+a)(c+x) D.) ax+bc E.) (a+b)(x+c) F.) ab(x+c)
Answers
Answer:
C.) (b+a)(c+x) = True
E.) (a+b)(x+c) = True
Step-by-step explanation:
all others are not equal.
Solve for X.........
Answers
Answer:
Hey there!
There is this equation, which states that the angle created by an inscribed angle is half the measure of the arc.
Thus, we can write: 60=5x-5
65=5x
x=13
Let me know if this helps :)
Answer:
x= 13
Step-by-step explanation:
Inscribed Angle =1/2 Intercepted Arc
30= 1/2 (5x-5)
Multiply each side by 2
60 = 5x-5
Add 5 to each side
65 = 5x
Divide by 5
13 =x
Alex is making an isosceles triangle-shaped pennant to support her school’s athletic team on sports day as shown below. Side ac is the same length as side an . Alex rotates the pennant 90 degrees clockwise to stick it to the wooden pole
Answers
Answer:
104°
Step-by-step explanation:
The marked angles have the same measure, so ...
(4x +10) = (7x -11)
21 = 3x . . . . . . . . . . . add 11-4x
7 = x . . . . . . . . . . . . . divide by 3
Then angle C is ...
C = (4x +10)° = (4(7) +10)° = 38°
The measure of angle A is 180° -2(38°) = 104°.
_____
That angle will have the same measure whether the pennant is rotated or not.
I need a bit help i don’t really get it
Answers
Answer:
Value of [tex]x[/tex] is $15$ degrees and measure of a vertical angle is $105$°
Step-by-step explanation:
These are vertically opposite angles which are congruent and hence equal.
Thus,
[tex]x+90=7x\\
\implies 90=6x\\
\implies x=\frac{90}{6}=\frac{30}{2}=15^o[/tex]
Find the measure of a vertical angle by putting the value of $x$ as $15$
Ernie walked 1 1/4 miles from his cabin to a park, then 1 1/2 miles around the park, and then back to his cabin. How many miles did he walk
Answers
Answer:
4 miles
Step-by-step explanation:
1 1/4 there + 1 1/2 around + 1 1/4 back= 4 miles
is -0.23 rational number whole number or integers
Answers
Answer:
rational number
Step-by-step explanation:
A whole number does not have a decimal part so it cannot be a whole number
Integers are whole numbers that are positive and negative plus zero
-.23 can be written as the ratio of integers
-23/ 100 so it is a rational number
Answer:
Rational
Step-by-step explanation:
A whole number does not have a decimal part so it cannot be a whole number
Integers are whole numbers that are positive and negative plus zero
-.23 can be written as the ratio of integers
-23/ 100 so it is a rational number
flying against the wind, a jet travels 4600 miles in 5 hours. flying with the wind, the same jet travels 4200 miles in 3 hours. what is the rate of the jet in still air and what is the rate of the wind?
Answers
Answer:
The rate of the jet in still wind is 1160 MPH and the rate of the wind is 240 MPH.
Step-by-step explanation:
Distance equals rate times time (d = rt)
Against the wind, the rate is:
4600 = r * 5
r = 4600/5 = 920 MPH
With the wind, the rate is:
4200 = r * 3
r = 4200/3 = 1400 MPH
Let W be the rate of the wind in MPH. We know that:
(rate of the jet against the wind) + (rate of the wind) = (rate of the jet with the wind ) - (rate of the wind), so:
920 + W = 1400 - W
2W = 480
W = 240 MPH
And the speed of the jet in still air would be:
1400 - 240 = 1160 MPH
PLEASE HELP ME Mathmath
Answers
Answer:
871 and 1/2 feet is correct
Step-by-step explanation:
Combine the like terms to create an equivalent expression. 5x - x
Answers
Answer:
the answer is 4x
Step-by-step explanation:
you are subtracting 1x
At a baseball game, hot dogs cost $2.25 and drinks cost $1.75. The total cost, t, for h hot dogs and d drinks can be described by the equation t=2.25h+1.75d. If Costas spent $18.25 and bought 5 hot dogs, how many drinks did he buy?
Answers
Answer:
He bought 4 drinks
Step-by-step explanation:
18.25= 2.25(5)+1.75d
18.25= 11.25+ 1.75d
18.25-11.25= 7
7= 1.75d
7/1.75
4=d
Answer:
4 drinks
Step-by-step explanation:
t = 2.25h + 1.75d
T = Total Cost
H = Hotdogs
D = Drinks
We have our total cost, which is $18.25 dollars
18.25 = 2.25h + 1.75d
We know Costas bought 5 hotdogs, so replace h with 5 and multiply :
2.25(5)
==> 11.25
Now that 11.25 dollars has been made, let's see how much money we need left to fit for the drinks.
18.25 - 11.25
==> 7
We need 7 dollars worth of drinks, so divide the cost by the amount we need to have.
7 / 1.75
==> 4
Castos needs to buy 4 drinks.
if the length of rectangle changes from 148.5cm to 144 cm. Find the percentage
change in the length.
Answers
Answer:
Original height = 144 cm
Increase height = 148.5 cm
Change in height = 148.5 - 144 = 4.5 cm
Percentage change = change/original ×100
= (4.5 / 148.5) × 100
= 3.03%
The height increased by 3.03%.
Step-by-step explanation:
Answer:
3%
Step-by-step explanation:
148.5 - 144 = 4.5
[tex]\frac{Difference}{Initial Amount}[/tex] × 100
[tex]\frac{4.5}{148.5}[/tex] × 100 = 3.03 ≈ 3%
I would really appreciate it if you would please mark me brainliest!
Have a blessed day!
Neal opened a savings account 11 years ago with a deposit of $2,335.69. The account has an interest rate of 4.3% compounded daily. How much interest has Neal earned? (3 points)
$1,412.52
$2,436.12
$1,375.75
$3,748.21
Answers
Answer: $1,412.52
Step-by-step explanation:
Formula to calculate the accumulated amount if P principal invested for t years at a rate of interest r that compounded daily is given by:-
[tex]A=P(1+\dfrac{r}{365})^{365t}[/tex]
Given: P= $2,335.69
r= 4.3%= 0.043
t= 11 years
Then,
[tex]A=2335.69(1+\dfrac{0.043}{365})^{365\times11}\\\\=2335.69(1+0.000117808219178)^{4015}\\\\=2335.69(1.000117808219178)^{4015}\\\\= 2335.69(1.6047566747)\\\\=3748.09044309\approx3748.21\\\\\Rightarrow\ A=\$3748.21[/tex]
Interest earned = A-P
= $3748.21- 2335.69.
= $1412.52
Hence, Neal earned $1,412.52 as interest.
Help me please!!! Weekly time card help. $11hr
Answers
Answer: 8hrs
Step-by-step explanation:
the sum of 81 and a number is greater than 4 times the same number
Answers
Answer: n=9
Step-by-step explanation:
81 = n>4*n
81 = 9(>4)*9
81 = 9*9
Kevin mowed 12 lawns and earned a total of $60.
Which rate represents the amount of money earned per lawn?
Answers
Answer:
$5
Step-by-step explanation:
$60 earned for moving 12 lawns
Amount of money per lawn is:
$60/12= $5Answer is amount per lawn is $5
Answer:
$5
or
$5 / 1 lawn
Step-by-step explanation:
The process is quite simple - especially since you already have half of the answer. The question says money per lawn. The creator of the problem gave away a lot of the answer. They already tell us the rate. Now all ou have to do is plug the numbers in:
Money per lawn
Money / lawns (The slash is used to represent per)
What is the money? $60. So plug that in:
$60 / lawns
How many lawns? 12. Plug that in:
$60 / 12 lawns
Now, all you have to do is either simplify the fraction or divide the denominator by the numerator - whichever one you prefer. In that case, the rate can be any of the following:
$5
$5 / 1 lawn
Hope this helps! Tell me if I am wrong!
The value 191.5638 rounded to the nearest hundredth is
191.564
191.5600
191.56
200
Answers
Answer:
191.56
Step-by-step explanation:
Given
191.5638
Required
Approximate
Approximating to the nearest hundredth implies that, only to digits after the decimal point is needed
This is:
191._ _
The third digit after the decimal point will approximated using the approximation rule;
Since, the third digit after the decimal point (3) is not up to 5, it'll be approximated to 0 and added to the second digit (6)
So, we have:
191.5 _
The next digit is calculated as 6 + 0 = 6
Hence, the full approximated number is 191.56
solve 1/2x + 7 = x - 3
Answers
Answer: x=20
Step-by-step explanation:
1/2x + 7 =x -3 add 3 to both sides
+3 +3
1/2x + 10 = x Subtract 1/2x from both sides
-1/2x -1/2x
10 = 1/2x
x = 20
Answer:
[tex]x=20[/tex]
Step-by-step explanation:
We can solve for x by simplifying the equation until we have x isolated on one side.
[tex]\frac{1}{2}x + 7 = x-3[/tex]
Subtract 7 from both sides:
[tex]\frac{1}{2}x = x-10[/tex]
Subtract x from both sides:
[tex]-\frac{1}{2}x = -10[/tex]
Multiply both sides by -2:
[tex]x = 20[/tex]
Hope this helped!
Strawberries cost $21.25 for 4 pounds. Find the unit rate. Round to the nearest cent if necessary.
Answers
Answer:
$5.31/lb
Step-by-step explanation:
Since 4 pounds cost $21.25, 1 pound of strawberries will cost 21.25 / 4 ≈ 5.31, therefore, the unit rate is $5.31/lb.
Answer:
$5.31 per pound.
Step-by-step explanation:
$21.25 for so
%21.25/4= $5.31
The answer is $5.31 per pound.
Solve the following equation for D. Be sure to take into account whether a letter is
capitalized or not.
Dm3 + n=r
Answers
Answer: capitalized
Step-by-step explanation:
Name the line segments
Answers
Answer:
EF, FG, GH, EG, FH, EH
Step-by-step explanation:
These are all the ones under def. line segment.
See the attachment. It will be helpful.
what integer is greater than -5
Answers
Answer:
-4,-3,-2,-1,0,+1,+2,+3..........
Step-by-step explanation:
-4 is greater than -5.
What is Number system?A number system is defined as a system of writing to express numbers.
An integer is the number zero, a positive natural number or a negative integer with a minus sign.
We need to find the integer which is greater than -5.
When we look into the number line we get an idea that the numbers with minus values are smaller than the positive values.
The greatest number with minus sign is smaller than the smallest number with minus sign.
-4 is greater than -5.
Not only -4 but the integers -4,-3,-2, -1, 0,1,2..... are greater.
Hence, -4 is greater than -5.
To learn more on Number system click:
https://brainly.com/question/22046046
#SPJ2
Wayne is planning a beach vacation. He budget's a total of $1,800 for the
vacation. Round-trip airfare for the trip will cost $610, while the all-inclusive
resort he plans to stay at will cost $238 per day. What is the maximum number
of days Wayne can stay at the resort and stay within his budget?
Answers
Answer:
5 days
Step-by-step explanation:
You subtract $610 from $1800. You should get 1190.
Then divide 1190 with 238.
The answer you get should be 5.
Answer:
5 days
Step-by-step explanation:
Solve the system by graphing
- 3x-y=2
solution (-2,0)
solution (0-2)
solution (2,0)
solution (02)
Answers
Answer:
(0,-2)
Step-by-step explanation:
Plug in each value for the equation
-3(0) - (-2) = 2
0 - (-2) = 2
2=2
.There is a 1/8 chance of a spinner landing on pink. Which statement is true? A. it is certain that the spinner lands on pink. B. it is impossible for the spinner to land on pink. C. it is likely that the spinner lands on pink. D. it is unlikely that the spinner lands on pink.
Answers
Answer:
it is unlikely that the spinner lands on pink.
Step-by-step explanation:
[tex]1- \frac{1}{8}\\ = 7/8[/tex]
There is 7/8 chance it is not going to land on pink
1 x 10^12 = 9 x 10^8 (8/d^2) solve for d
Answers
Answer: Go here https://quickmath.com/webMathematica3/quickmath/equations/solve/basic.jsp
Step-by-step explanation:
It will show you how
An electronic product takes an average of 4 hours to move through an assembly line. If the standard deviation is 0.5 hours, what is the probability that an item will take between 2.8 and 4.3 hours to move through the assembly line
Answers
Answer:
0.7176
Step-by-step explanation:
We solve this question, using z score formula.
Z score formula = (x - μ)/σ
where x is the raw score
μ is the population mean
σ is the population standard deviation.
For z1, where x1 = 2.8, μ = 4, σ = 0.5
z score formula = (2.8 - 4)/0.5
= -2.4
We find the probability of the z score using the z score table.
P(x = 2.8) = P(z = -2.4)
= 0.0081975
For z2, where x2 = 4.3, μ = 4, σ = 0.5
z score formula = (4.3 - 4)/0.5
= 0.3/0.5
= 0.6
We find the probability of the z score using the z score table.
P(x = 4.3) = P(z = 0.6)
= 0.72575
The probability that an item will take between 2.8 and 4.3 hours to move through the assembly line is calculated as:
= 2.8 < x < 4.3
= P(z = 0.6) - P(z = -2.4)
= 0.72575 - 0.0081975
= 0.7175525
Approximately ≈ 0.7176
Therefore, the probability that an item will take between 2.8 and 4.3 hours to move through the assembly line is 0.7176