The formula upper a equals 23.1 e superscript 0.0152 ta=23.1e0.0152t models the population of a us state, a, in millions, t years after 2000.

a. what was the population of the state in 2000?
b. when will the population of the state reach 28.328.3 million?

a)

b)

So for this case the answer would be 13.347 years, the population will be 28.3 million and ye year would be 2000+13.347 and that would be approximately in 2014

Step-by-step explanation:

For this case we assume the following model:

Where t is the number of years after 2000/

Part a

For this case we want the population for 2000 and on this case the value of t=0 since we have 0 years after 2000. If we rpelace into the model we got:

So then the initial population at year 2000 is 23.1 million of people.

Part b

For this case we want to find the time t whn the population is 28.3 million.

So we need to solve this equation:

We can divide both sides by 23.1 and we got:

Now we can apply natural log on both sides and we got:

And then for t we got:

So for this case the answer would be 13.347 years, the population will be 28.3 million and ye year would be 2000+13.347 and that would be approximately in 2014

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step-by-step explanation: