Write the equation in exponetial function

First let's solve for the rate, "b", by setting up a ratio with the two points given:

16.875/7.5=(ar^3)/(ar)

2.25=r^2

r=1.5

Now we need to solve for the initial value a using either point given...

7.5=a(1.5)^1

7.5=1.5a

a=5

So now we have solved for both variables and have a complete equation:

y=5(1.5)^x

With a continuous thought process.