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

Question

x. y

0. 4

1. 8

2. 16

3. 32

Answer 1

Katelyn:

y = Ae^bx represents the general equation of an exponential function.

For x = 0, y =4. So. 4=Ae^b*0. so 4=A*e⁰ 4=A*1 A=4

For x=1, y=8. So 8 = 4*e^b*1 8 = 4*e^b or e^b = 2. I'll let you solve for b. Once you have b, you can plug in A=4 and whatever b is to get the desired equation. You will need the identity e^ln(u)*x = u^x when you simplify. Make sure to check that the function works for each value in the table. Let me know if you need help!

Answer 2

y=2^x+2