Answer:
[tex]y = 66.25(1.11)^x[/tex]
Step-by-step explanation:
Let's plug in 9 for x and 171 for y into the given exponential equation:
y = [tex]ab^x[/tex]
171 = [tex]ab^9[/tex]
Now do the same with (10, 190):
190 = [tex]ab^{10}[/tex]
Write them both in terms of a and set them equal:
a = 171/[tex]b^9[/tex]
a = 190/[tex]b^{10}[/tex]
171/[tex]b^9[/tex] = 190/[tex]b^{10}[/tex]
Multiply both sides by [tex]b^{10}[/tex]:
171b = 190
b = 190/171 = 10/9 ≈ 1.11
Plug this in to find a:
a = 171 / (10/9)^9 ≈ 66.25
So, the exponential model is:
[tex]y = 66.25(1.11)^x[/tex]
