Question

The formula A = 223e0.023t models the population of a particular city, in thousands, t years after

1998. When will the population of the city reach 287 thousand? [Hint: round to nearest year.]

Answer 1

Answer: 2005

Explanation:

To find out when the population of the city will reach 287 thousand, we need to solve the equation A = 223e0.023t for t.

First, we divide both sides of the equation by 223 to get:

e0.023t = A/223

Next, we take the natural logarithm of both sides of the equation to get:

ln(e0.023t) = ln(A/223)

Using the property of logarithms that ln(ab) = b ln(a), we can simplify the equation to:

0.023t ln(e) = ln(A/223)

Since ln(e) = 1, we can simplify further to:

0.023t = ln(A/223)

Now we can solve for t by dividing both sides of the equation by 0.023:

t = ln(A/223) / 0.023

Substituting A = 287, we get:

t = ln(287/223) / 0.023

Using a calculator, we get:

t ≈ 7

Therefore, the population of the city will reach 287 thousand approximately 7 years after 1998, which is 2005.