Question

The graph of an exponential function passes through the point (0,15) and (1,10). What is the equation of the exponential function that models the curve that passes through these two points? Explain your answer using complete sentences.

Answer 1

`y=15((2)/(3))^x`

Explanation:

we know that

The equation of a exponential function is of the form

`y=a(b^x)`

where

a is the initial value or y-intercept

b is the base of the exponential function

In this problem we have

`a=15` ----> the y-intercept is given

substitute

`y=15(b^x)`

we have the other ordered pair (1,10)

substitute the value of x and the value of y and solve for b

`10=15(b^1)\\10=15b`

`b=(10)/(15)=(2)/(3)`

substitute

`y=15((2)/(3))^x`

see the attached figure to better understand the problem