Question

An exponential relationship y = f(x) has a l-unit percent change of 12% with f(0) = 28.i. Define a formula for function f modeling this relationship. Be sure to use function notation, and be sure to use the correct function name.

Answer 1

$f(x)=28\times(1.12)^x$

The percent change is 12%, meaning after each interval x the new value is 112% times the previous value. This can be expressed as (for x = 1)

$\text{new value=28}\times\frac{112}{100}$

when x = 2 the above value becomes the "previous value" and therefore, the new value will be

$\text{new value =(28}\times\frac{112}{100})\times\frac{112}{100}$

when the above becomes the previous value the new value then will be

$\text{new value =((28}\times\frac{112}{100})\times\frac{112}{100})\times\frac{112}{100}$

and so on until we have x number of 122/100 =1.12 terms. Then the new value for any x can be written as

$\text{new value for any x=28(}\frac{112}{100})^x$

or

$f(x)=28(1.12)^x$