Question

Which of the following models the rising population of a city with 8,000 residents when the annual growth rate is 4%?y = 8000(0.04)xy = 800(1.04)xy = 8000(1.04)xy = 1.04(8000)x

Answer 1

Explanation

We are given the following:

`\begin{gathered} initial\text{ }population(a)=8000 \\ r=4\%=0.04 \end{gathered}`

We are required to determine the model with the given data.

We know that the model is an exponential function given as:

`\begin{gathered} y=ab^x \\ where \\ b=1+r \end{gathered}`

Therefore, we have:

`\begin{gathered} y=ab^x \\ y=8000(1+0.04)^x \\ y=8000(1.04)^x \end{gathered}`

Hence, the answer is:

`y=8,000(1.04)^(x)`