Write an exponential function in the form y=ab^x that goes through the points (0,18) and (8,4608)

Answer 1

y=ab^x

18=ab⁰=a(1)=a

4608=18b⁸

b⁸=4608/18=256=2⁸

b=2

y=18(2^x)

Answer 2

y = ab^x

Plug in the given (x,y) points in the equation and solve for a and b:

y(0) = ab⁰ = a = 18

y(8) = ab⁸ = 18b⁸ = 4608

Solve for b: b = (4608/18)^1/8 = 2

The function is y = 18(2)^x

Check: y(8) = 18(2)⁸ = 4608