Question

What is the constant ratio of an exponential curve that passes through the points (0,3)

and (5,96)?

Answer 1

`r = 2`

Explanation:

Given

`(x_1,y_1) = (0,3)`

`(x_2,y_2) = (5,96)`

Required

Determine the common ratio

An exponential function is of the form.

`y(x) = ar^x`

For:

`(x_1,y_1) = (0,3)`

We have:

`3 = a * r^0`

`3 = a * 1`

`a= 3`

For

`(x_2,y_2) = (5,96)`

We have:

`96 = ar^5`

Substitute 3 for a

`96 = 3 * r^5`

Divide both sides by 3

`(96)/(3) = (3 * r^5)/(3)`

`32 = r^5`

Express 32 as an exponent of 2

`2^5 = r^5`

By comparison

`2 = r`

`r = 2`