Answer: f(3)
Step-by-step explanation:
First find the formula for the rate of change by taking the derivative of 2^x. Let f(x) equal some hypothetical y-value, then take the natural log of both sides.
[tex]y=2^x\\\ln(y)=x \ln(2)[/tex]
Implicitly differentiate the left side and take the derivative of the right side
[tex]\frac{y'}{y} =\ln(2)[/tex]
Multiply both sides by 'y' which was defined as 2^x
[tex]y'=\ln(2)*2^x[/tex]
Plug in x = 2 and x = 3 to see which slope is larger
[tex]y'=\ln(2)*2^2=4\ln(2)\\y'=\ln(2)*2^3=8\ln(2)[/tex]
