Question

The initial population of the town was estimated to be 12,500 in 2005. The population has increased by about 5.4% per year since 2005.

Formulate the equation that gives the population, A(x) , of the town x years since 2005. If necessary, round your answer to the nearest thousandth.

A(x)=__(_)^x

Answer 1

Answer:

$A(x) = 12500(1.054)^x$

Step-by-step explanation:

Exponential equation for population growth:

Considering a constant growth rate, the population, in x years after 2005, is given by:

$A(x) = A(0)(1 + r)^x$

In which A(0) is the population in 2005 and r is the growth rate, as a decimal.

The initial population of the town was estimated to be 12,500 in 2005.

This means that $A(0) = 12500$

The population has increased by about 5.4% per year since 2005.

This means that $r = 0.054$

So

$A(x) = A(0)(1 + r)^x$

$A(x) = 12500(1 + 0.054)^x$

$A(x) = 12500(1.054)^x$