Question

The formula A = 265e0.039t models the population of a particular city, in thousands, t years after 1998. When will the population of the city reach 457 thousand?

Answer 1

In 2012 the population of the city reach 457 thousand.

Explanation:

We are given with equation A= 265
`e^(0.039t)`

Here it is given that A is 457.

So, plug in A as 457 and solve for 't'.

457= 265
`e^(0.039t)`

Divide both sides by 265.

1.7245283 =
`e^(0.039t)`

Now, take natural log on both sides,

ln(1.7245283)= ln(
`e^(0.039t)`)

0.5449535= 0.039t

Divide both sides by 0.039

t=13.97...

So, 't' is years after 1998.

So, 1998+13.97 =2011.97...

If we round to nearest years, we do get 2012.