Question

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

Answer 1

ANSWER:

a. 21.2

b. 2008

STEP-BY-STEP 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:

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

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