Question

Twenty years ago a small town in Texas had a population of 10,000. The population has increased 8% each year since then. What is the growth factor that would be used to solve this problem?

Answer 1

The growth factor is one plus or minus (depending on increase or decrease) the percent written as a decimal. In this case 1-0.08= 0.92

Answer 2

1.08

Explanation:

We have been given that 20 ears ago a small town in Texas had a population of 10,000. The population has increased 8% each year since then.

We can see that population is increasing exponentially, so we will use exponential function to write formula for our given information.

`y=a*(b)^x`, where,

a = Initial value,

b = For growth b is in form (1+r), where r is growth rate in decimal form.

Let us convert our given growth rate in decimal form.

`8\%=(8)/(100)=0.08`

Upon substituting our given values in exponential function formula we will get,

`y=10,000*(1+0.08)^x`

`y=10,000*(1.08)^x`

We can see that value of b is 1.08, therefore, growth factor for our given problem is 1.08.