Question

change f(x) = 30(0.94)^x
to an exponential function with base e.

Answer 1

General form of exponential function is \[y= A e^{kx}\]

Answer 2

Which, by index laws can be expressed as

Answer 3

\[y=A[e^{k}]^{x}\]

Answer 4

remember when you raise one power to another power, you multiply the powers.

Answer 5

Now it's just a matter of matching terms.

Answer 6

A=30 (obviously)

Answer 7

e^(k) = 0.94 ---> k = ln(0.94) = -0.06188 (to 5dp)

Answer 8

So, \[y= 30e^{-0.06188x}\]

Answer 9

thank you so much! makes perfect sense