Question

A) and 2000 the population of the state was blank million

Answer 1

a. 21.2

b. 2008

Explanation:

We have that the function that models the population is the following:

`A=21.2\cdot e^(0.0407t)`

a.

In the year 2000, t = 0, we substitute and calculate the population, just like this:

`\begin{gathered} A=21.2\cdot e^(0.0407\cdot0) \\ \\ A=21.2\cdot e^0 \\ \\ A=21.2\cdot1 \\ \\ A=21.2 \end{gathered}`

In 2000, the population of the state was 21.2 million.

b.

Now, in this case A = 29.8, we solve for t, just like this:

`\begin{gathered} 29.8=21.2\cdot \:e^(0.0407\cdot \:t) \\ \\ e^(0.0407\cdot\:t)=(29.8)/(21.2) \\ \\ 0.0407t=\ln\left((29.8)/(21.2)\right) \\ \\ t=(\ln\left((29.8)/(21.2)\right))/(0.0407) \\ \\ t=8.37 \end{gathered}`

Therefore, it would be 8 years after 2000. The population of the state will reach 29.8 million in the year 2008