Question

Write an exponetial function for the points (1,7.5) (3,16.875) in the form y=a•b^x

Answer 1

16.875=ab^3  (divided by what follows)

7.5=ab^1  gives you:

2.25=b^2

b=1.5 now we can solve for a...

7.5=a(1.5^1), a=5 so the function is:

y=5(1.5^x)

Answer 2

First, understand that an exponential function is one that is of the form y = a*b^x + c

So, you have two points
For the first point: 7.5 = a*b^1 + c ==> a*b + c = 7.5 = 15/2
For the second: 16.875 = a*b ^3 + c ==> a*b^3 + c = 16.875 = 135/8
Notice that 2 = 2^1 and 8 = 2^3...
also 15 = 5 * 3^1 and 135 = 5 * 27 = 5*3^3
So, let's leave c =0 (to make the function less complex)
then a = 5, b = 3/2
so: y = 5 (3/2)^x