table to exponential function

Question

Find the equation of the exponential function represented by the table below:

x y

0 5

1 10

2 20

3 40

Answer 1

General form of exponential expression:

y = Ae^kx

y(0) = Ae⁰= A(1) = 5 --> A = 5

y(1) = 5e^k = 10 --> e^k = 10/5 = 2 --> ln(e^k) = ln(2) --> k = ln(2)

y = 5e^ln(2)x = 5(e^ln(2))^x = 5(2)^x

y = 5(2)^x

y(2) = 5(2)² = 5•4 = 20 checks

y(3) = 5(2)³ = 5•8 = 40 checks

Answer 2

General form of exponential expression:

y = Ae^kx

y(0) = Ae⁰= A(1) = 5 --> A = 5

y(1) = 5e^k = 10 --> e^k = 10/5 = 2 --> ln(e^k) = ln(2) --> k = ln(2)

y = 5e^ln(2)x = 5(e^ln(2))^x = 5(2)^x

y = 5(2)^x

y(2) = 5(2)² = 5•4 = 20 checks

y(3) = 5(2)³ = 5•8 = 40 checks