Exponential function y=c(bx)

Question

Determine the exponential function y=c(bx) that goes through the points (−2,16) and (1,54). Algebraic work 

Answer 1

If y=cb^x then we must use a system of equations with the given points.

Equation 1: using (1,54) we have 54=cb

Equation 2: using (2,16) we have 16=cb^-2=c(1/b²)

Solving for c in equation 1 we have (54/b)=c

We plug this into the second equation to obtain: 16=(54/b)(1/b²)=54/b³

Solving for b³ we get b³=54/16=27/8 yielding b=3/2.

Using equation 1 we get 54=c(3/2) and solving for c we get c=36

Thus: y=36(3/2)^x