The population of Fantasy City doubles each month. When will the city be half populated if it will be fully populated in 10 months.

Answers

Answer 1

Using an exponential function, it is found that the city will be half populated in 9 months.

The population of Fantasy City doubles each month, hence, after t months, the population is given by:

[tex]P(t) = P(0)2^{t}[/tex]

In which P(0) is the initial population.

Fully populated in 10 months, hence, the full population is:

[tex]P(10) = P(0)2^{10} = 1024P(0)[/tex]

Hence, half populated is [tex]P(t) = \frac{1024P(0)}{2} = 512P(0)[/tex], hence:

[tex]P(t) = P(0)2^{t}[/tex]

[tex]512P(0) = P(0)2^{t}[/tex]

[tex]2^t = 512[/tex]

[tex]2^t = 2^9[/tex]

[tex]t = 9[/tex]

The city will be half populated in 9 months.

To learn more about exponential functions, you can take a look at https://brainly.com/question/25537936


Related Questions

Help help help math math

Answers

Answer:

y=-1/2x-3

Step-by-step explanation:

Let's pick two points for slope.

[tex]\frac{-1+3}{-4-0}[/tex]

[tex]\frac{2}{-4}[/tex]

For the y-inctercept, the line intersect at the y-axis at (0,-3)

CHECK:

[tex]y=-\frac{1}{2} (-4)-3[/tex]

[tex]y=2-3[/tex]

[tex]y=-1[/tex]

Lisa's living room is 21 feet wide. If the length is 4 feet less than twice the width, what is the area of her living room?

square feet

Answers

Answer:

21+21=42

42-4=38

21x38=798sq ft

Step-by-step explanation:

42-4=38 so your answer is 38

Wiebe Trucking. Inc. is planning a new warehouse to serve the west. Denver, Santa Fe, and Salt Lake City are under consideration. For each location, annual fixed costs (rent, equipment. and Insurance) and average variable costs per shipment (labor, transportation and utilities) are listed in the following table. Sales projection is range from 550,000 to 600,000 shipments per year.
a. Plot the total cost curves for all the locations on a single graph.
b. Which city provides the lowest overall costs?

Answers

The total cost curve shows the cost of total shipment from the different

cities.

a. Please find attached the graph of the total cost to quantity of shipment created with MS Excel.

b. The city that provides the lowest overall cost is; Salt Lake City.

Reasons:

The given parameters are;

The number of shipment per = From 550,000 to 600,000 per year

The given table is presented as follows;

[tex]\begin{tabular}{|l|c|c|c|}Location&Annual Fixed Costs&Variable Cost \\Denver&\$5,000,000&\$4.65 \\Santa Fe&\$4,200,000&\$6.25\\Salt Lake City&\$3,500,000&\$7.25\end{array}\right][/tex]

a. Required:

The plot total cost curve for the locations on a single graph.

Solution:

Please find attached the graph of the total cost curves created with MS Excel

b. Required:

The city that provides the lowest overall cost.

Solution:

The two cities with the lowest overall costs are Denver and Salt Lake City.

From the total cost curve, the area under the curves are;

Area under the curve for Denver;

(7557500 + 7790000) ÷ 2 × 50,000 = 383687500000

Area under the curve for Salt Lake City

(7487500 + 7850000) ÷ 2 × 50,000 = 383437500000

Therefore;

Salt Lake City provides the lowest overall costs.

Learn more about total cost curves here:

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Which graph best represents the equation x2 + (y – 1)2 = 3?

Answers

Answer:

Step-by-step explanation:

assuming the equation is x^2 + (y - 1)^2 = 3

please help me im giving brainliest

Answers

Step-by-step explanation:

49² + 98 + 1 compared to a² + 2ab + b² means that

a = 49

b = 1

as this would be 49² + 2×49×1 + 1² = 49² + 98 + 1

so, we have actuality

(49 + 1)² = 50² = 2500

Answer:

49² + 98 + 1 compared to a² + 2ab + b² means that

a = 49

b = 1

as this would be 49² + 2×49×1 + 1² = 49² + 98 + 1

so, we have actuality

(49 + 1)² = 50² = 2500

Step-by-step explanation:

The amount of money charged to borrow money, expressed as a percentage,
is called the
A. collateral
B. interest rate
O C. principal
D. loan term

Answers

Answer:

Interest rate

Step-by-step explanation:

The amount owed is called the principal and the price of borrowing money is called interest. Some people spend a day's pay (or more) per week repaying the interest and principal owed on car loans, credit card bills, student loans, and other consumer debts.

Help, please

Erica solved the equation −5x − 25 = 78; her work is shown below. Identify the error and where it was made.

−5x − 25 = 78
Step 1: −5x − 25 − 25 = 78 − 25
Step 2: −5x = 53
Step 3:negative five times x over negative five = fifty-three over negative five
Step 4: x = negative fifty-three over five

Answers

Answer:

The first step.

Step-by-step explanation:

24-(8÷2)+6 I need help, please somebody answer

Answers

Answer:

26

Step-by-step explanation:

STEP

1

:

4

Simplify —

1

Equation at the end of step

1

:

(24 - 4) + 6

STEP

2

:

Final result :

26

ANSWER: 26

EXPLANATION:

To solve this we need to use order of operations, also known as pemdas

Parentheses
Exponents
Multiplication
Division
Addition
Subtraction

You do that in order.

So first solve what in the parentheses,

8 divided by 2 is 4

So now we have

24 - 4 + 6

I know addition is written first in PEMDAS but you’re supposed do go left to right when that’s all you have left.

So

24 - 4 = 20

And

20 + 6 = 26

Hope this helps. If you have questions I’m here to answer

For shipping the retailer charges a $4.95 flat fee or 5.75% of the total purchase, whichever is greater. If Lucia's total purchase is $78.99, how much shipping will she pay? PLEASE ANSWER ASAP

Answers

ANSWER: $4.95

EXPLANATION:

So it’s asking us to find out if $4.95 dollars is more than 5.75% of 78.99.

So we need to find 5,75% of 78.99

To find percentage turn the percent into a decimal.

5.75% become 0.575

Now we have 0.575 x 78.99

That is 45.41925

Move the decimal over again and you get 4.541925

Round to the nearest hundredth to get

$4.54

$4.54 < $4.95

So the answer is &4.95

30=2y+16 simplify your answer as much as possible

Answers

Answer:

y=7

Step-by-step explanation:

LAST ATTEMPT IM MARKING AS BRAINLIEST!! ( use the scale factor to write the ordered pairs after the dilation )

Answers

A = (0,0)
B = (-15,10)

can anyone help me please? i have 14 more minutes to finish this can anyone help?

Answers

Answer:

B

Step-by-step explanation:

A is 3-2 which is 1, not 5.

C is 3(2), which is 6, not 5.

D is 6, which is not 5.

-hope it helps

Answer:

B

Step-by-step explanation:

I need help with math

Answers

51+60= 111 Answers fast rights

help me my due is In 10 minutes. I don’t know ​

Answers

Step-by-step explanation:

You take the first amount ex: 80 then times 0.2 (20%->0.2) and ad the result to 80

A boat is heading towards a lighthouse, whose beacon-light is 134 feet above the
water. From point A, the boat's crew measures the angle of elevation to the beacon,
16°, before they draw closer. They measure the angle of elevation a second time from
point B at some later time to be 21°. Find the distance from point A to point B.
Round your answer to the nearest foot if necessary.

Answers

this may help you very much

Amanda went to the Farmer’s market with her family. She had $5.00 to spend and decided she wanted to spend it on peaches. Each peach cost 68 cents. How many peaches could she buy ?

Answers

She could buy 7 peaches because 7 times .68= $4.76. She couldn’t buy another peach because she doesn’t have the extra ¢.68

2) through: (-4, 5) and (-5,0
what is the slope intercept form of the line

Answers

Answer:

hello

Step-by-step explanation:

say hell-o

Need help with a math problem If doing 5 stars and a good rating

Answers

Answer:

16:1

Step-by-step explanation:

Since there are 85 total people and 80 are students that means 5 are chaperones.(85-5) Therefore the ratio of students to chaperones is 80:5 or simplified 16:1.

correct?````````````````````````````

Answers

Yeah you’re already correct

A line with a slope of 10 passes through the point (0,4). What is its equation in
slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.

Answers

Answer:

y=10x+4

Step-by-step explanation:

y-y1=m(x-x1)

y-4=10(x-0)

y-4=10(x)

y-4=10x

y=10x+4

On a number line, where would
4/5
be located? Choose all answers that make
a true statement.

Answers

The answer is To the right of 3/5
3+1= 4 so it’s like 1,2 so
It’s the right of 3/5
only a and b are correct!

multiply (2x+3y)(x-y)​

Answers

Answer:

2x^2 +xy - 3y^2

Step-by-step explanation:

2x(x-y) +3y(x-y)

2x^2+xy - 3y^2

I'm giving out a lot of points for this one!

Answers

Answer:

Step-by-step explanation:

AVERAGE rate of change looks only at the endpoints

m = Δy/Δx

m = (1.2 x 10⁶ - 0.35 x 10⁶) / (2640 - 1955)

m = 0.35 x 10⁶/ 685

m = 1241  beings / year

Solve the equation for​ z, where z is restricted to the given interval.

[tex]y=7sinz[/tex], for z in [tex][-\frac{\pi }{2}, \frac{\pi }{2} ][/tex]

Answers

[tex]y = 7sin(z)\implies 0 = 7sin(z)\implies 0=sin(z)\implies sin^{-1}(0)=sin^{-1}[sin(z)] \\\\\\ sin^{-1}(0)=z\implies 0=z[/tex]

Sort the sequences according to whether they are arithmetic, geometric, or neither.

Answers

Answer:

arithmeticneithergeometricarithmeticgeometric

Step-by-step explanation:

Arithmetic sequences have a common difference. Often, checking for that is the easiest. Geometric sequences have a common ratio. If there is neither a common difference nor a common ratio, then the sequence is not one of these types.

The difference or ratio refers to the relation of a term in the sequence to the one before it. For example, 94.1 -98.3 = -4.2. If the same difference exists for subsequent pairs of terms, then the difference is said to be "common." Likewise, 3.5/1.75 = 2. If the same ratio exists for subsequent pairs of terms, it is a "common" ratio.

__

98.3, 94.1, ... -- arithmetic (common difference = -4.2)

1, 0, -1, 0, ... -- neither

1.75, 3.5, ... -- geometric (common ratio = 2)

-12, -10.8, ... -- arithmetic (common difference = -1.2)

-1, 1, ... -- geometric (common ratio = -1)

Answer: Arithmetic (98.3,94.1, 89.9, 85.7,...)  (-12,-10.8, -9.6,-8.4)

Geometric (1.75,3.5,7, 14) (-1,1,-1,1,...)

Neither (1,0,-1,0,...)

Step-by-step explanation:

I guarantee these are correct.

What is with simplifying
-3p + 6p

Answers

Answer:

-3p+6p=3p

Step-by-step explanation:

It's just like saying -3+6,

but just with the p.

-3+6=3

therefore the answer is 3p

Find the length x…..

Answers

Answer:

x = 4

Step-by-step explanation:

6 : 4.5 = 4 : 3

x : 3 = 4: 3

x= 4

Alexa spins a spinner that is divided into 6 equally sections: 2 red, 1 green, and 3 blue. What is the probability that Alexa spins a red or green?

Answers

Answer:

probability = 1/2 or 50%

Step-by-step explanation:

number of red + number of green = 2 + 1 = 3

Probability of landing on a red or green = 3/6 = 1/2

Red

Step-by-step explanation:Red

Is the sum of 5x⁴ + x³ and 2x³ + x² a trinomial expression. If it is true, justify your answer.​

Answers

Answer:

The sum is a trinomial. It has three terms of different powers in variable "x" and three non zero constants as coefficients.

Step-by-step explanation:

(5x⁴ + x³) + (2x³ + x²) = 5x⁴ + 3x³ + x²

The sum of 5x⁴ + x³ and 2x³ + x² is a trinomial expression that is  5x⁴ + 3x³ + x²

What is an expression?

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The sum is a trinomial. It has three terms of different powers in variable "x" and three non zero constants as coefficients.

We are given the expression as;

5x⁴ + x³ and 2x³ + x²

We need to find of the sum of the expression as;

(5x⁴ + x³) + (2x³ + x²)

= 5x⁴ + 3x³ + x²

The sum of 5x⁴ + x³ and 2x³ + x²  is  5x⁴ + 3x³ + x²

To know more about an expression follow;

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#SPJ2

solve for x where xe(0,2pi). state exact answers.
b)
[tex] \frac{1}{ \sqrt{3} } \sin(2x) + \cos(x) = 0[/tex]
e)
[tex]3 \cos(x) + \tan(x) = 0[/tex]
Note: for question e, get this equation to a point ready for factoring or to use the quadratic formula, then stop. make sure its in standard form.​

Answers

Answer:

that's the correct answer

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