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

Answer:

9672

Step-by-step 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.