SOLUTION:
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:
[tex]f(x)\text{ = 1800 }(1\text{ + }\frac{9.9}{100})^t[/tex]
Part B :
Use your function to predict the population of Star, ID in 2050
[tex]\begin{gathered} \text{Given } \\ f(x)\text{ = 1800 ( 1 + }\frac{9.9}{100}^{})^t \end{gathered}[/tex]
The year 2050 means that t= 50, we have that:
[tex]\begin{gathered} f(x)=\text{ 1800 ( 1 + }\frac{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}[/tex]
Part C:
The function:
[tex]g(x)\text{ = 11000 ( 1}.056)^x[/tex]
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:
[tex]f(x)=1800(1.099)^{50}[/tex]
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.
