The formula A = 23.1 e 0.01521 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 28.3 million?

a. In 2000, the population of the state was__million.
b. The population of the state will reach 28.3 million in ___.

- The population in 2001 is 23.1 million

- It will reach 28.3 million in 2013

Step-by-step explanation:

Given

Solving (a): Population in 2000.

This implies that

So, we have:

Solve the exponent

The population in 2001 is 23.1 million

Solving (b): When will it reach 28.3 million

This implies that:

So, we have:

Divide both sides by 23.1

Take natural logarithm of both sides

Rewrite as:

So:

Make t the subject

Add the value of t to 2013 to get the actual year

It will reach 28.3 million in 2013

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