Question

The population of a town was 10,000 in 2018. Each year the town's population grows by 23%. Let x=0 be the year 2018. Create the exponential function that will give these population values. (Be sure to use function notation, f(x)= ____ in your answer.)

Answer 1

`f(x)=10000(1.23)^x`

Explanation:

We are going to apply algebra to solve for the exponential growth

we know that the expression for the exponential formula is

`y = ab^x.`

where

a = the amount before measuring growth or decay

= 10,000

r = growth or decay rate = 23%= 0.23

x = number of time intervals that have passed

since this problem is on the growth we are going to replace "b" with (1+r), likewise for decay (1-r)

hence the formula becomes

`y = a(1+r)^x.`

`f(x)=10000(1+0.23)^x \\\\f(x)=10000(1.23)^x`

The expression that will give the population value is

`f(x)=10000(1.23)^x`