Question

. The population of Star, ID was 1800 people in the year 2000. The population has been growing at a rate of 9.9% annually. a. Write a function that models the population of Star, ID in years since 2000.b. Use your function to predict the population of Star, ID in 2050.c. The function g(x)=11000(1.056)^x models the population of Eagle, ID in years (x) since 2000. Which city is growing faster? How do you know?

Answer 1

Step 1:

In this question, we have the following:

Step 2:

Part A:

The function that models the population of Star, ID in years since 2000 is:

`f(x)\text{ = 1800 }(1\text{ + }(9.9)/(100))^t`

Part B :

Use your function to predict the population of Star, ID in 2050

`\begin{gathered} \text{Given } \\ f(x)\text{ = 1800 ( 1 + }(9.9)/(100)^{})^t \end{gathered}`

The year 2050 means that t= 50, we have that:

`\begin{gathered} f(x)=\text{ 1800 ( 1 + }(9.9)/(100))^(50) \\ f(x)=1800X(1+0.099)^(50) \\ f(x)\text{ =}1800(1.099)^(50) \\ f(x)=201,909.6734 \\ f(x)\approx\text{ 201, 910 ( to the nearest whole number)} \end{gathered}`

Part C:

The function:

`g(x)\text{ = 11000 ( 1}.056)^x`

models the population of Eagle, ID in years (x) since 2000.

Which city is growing faster? How do you know?

Answer:

From this equation, we can see that the growth rate is 5.6% annually.

Comparing this, with the initial function:

`f(x)=1800(1.099)^(50)`

We can see that the annual growth rate of f(x) is 9.9 %

CONCLUSION:

The population of Star ID, with the function, g (x) has a faster growth rate.