Answer:
[tex]r = 2[/tex]
Step-by-step explanation:
Given
[tex](x_1,y_1) = (0,3)[/tex]
[tex](x_2,y_2) = (5,96)[/tex]
Required
Determine the common ratio
An exponential function is of the form.
[tex]y(x) = ar^x[/tex]
For:
[tex](x_1,y_1) = (0,3)[/tex]
We have:
[tex]3 = a * r^0[/tex]
[tex]3 = a * 1[/tex]
[tex]a= 3[/tex]
For
[tex](x_2,y_2) = (5,96)[/tex]
We have:
[tex]96 = ar^5[/tex]
Substitute 3 for a
[tex]96 = 3 * r^5[/tex]
Divide both sides by 3
[tex]\frac{96}{3} = \frac{3 * r^5}{3}[/tex]
[tex]32 = r^5[/tex]
Express 32 as an exponent of 2
[tex]2^5 = r^5[/tex]
By comparison
[tex]2 = r[/tex]
[tex]r = 2[/tex]
