Question

In 2000, the population of a town was 8914. The population is expected to grow at a rate of 1.36% each year. What is the population of the town in 2006? Round the answer to the nearest whole number.

Answer 1

Answer: 9667

Just took the test. :)

Answer 2

9672

Explanation:

Population growth can be represented by the equation
`A=A_0e^(rt)`. We know the rate at which it grows is 1.36%. For the formula, we use the decimal conversion which is r=0.0136. We find the amount of time that has passed between 200 and 2006 is t=6 years. In this context, the starting population is
`A_0=8914`. We substitute and solve for A.

`A=A_0e^(rt)\\A=8914e^(0.0136(6)))`

`A=8914e^(0.0816)[`

We solve with a calculator by evaluating the exponent first and then multiplying by 8914.

`A=8914e^(0.0816)[` .

`A=8914(1.08502171433)[`

The solution is 9671.88356154 but we round to 9672.