Question

In 2005, the population of a town was 17,500. Suppose the population grows exponentially at a rate of 3% per year. Write an equation to model this situation, let x represent the number of years since 2005.

Answer 1

Answer:

The expression is:  $p(x) = 17500*(1.03)^x$

Step-by-step explanation:

Since we're starting our count in 2005, then let's call that year 0 and every year after that will be 2005 + x, where t grows from 0 as an integer.

In 2005 the population is:

$p(0) = 17500$

In 2006 the population is:

$p(1) = 17500*(1 + \frac{3}{100}) = 17500*(1.03)$

In 2007 the population is:

$p(2) = p(1)*(1.03) = 17500*(1.03)*(1.03) = 17500*(1.03)^2$

In 2008 the population is:

$p(3) = p(2)*(1.03) = 17500*(1.03)^2*(1.03) = 17500*(1.03)^3$

We can notice a pattern that the population pf the city is equal to the number of the starting population multiplied by the rate of change powered by the number of years after 2005. Therefore a generic expression for the population of that town can be written as:

$p(x) = 17500*(1.03)^x$