(Business) Calculus experts please help! Problem haunting me all day!

Question

The following problem has been disheartening me the entire day. It is one of the few things in all my time being introduced new concepts in any of my mathematics class where I have 0% idea how to do. Please help!

 

"The revenue R(x) in millions of dollars of a department store starting this year is projected by

 

R(x) = 1548e^0.0617x

 

Where x is the number of years from now. At what rate will the revenue be changing 6 years from now? Show all work."

Answer 1

Close -

 

The derivative of e^x is e^x at every value of x.  the derivative does not have the 0.0617 as a factor.

 

Thus, the answer at 6 years is about $624,507.77

 

 

 

 

 

Answer 2

The Rate of Change of a function is the derivative of the function. The first derivative of  R(x) = R'(x) = 1548*(0.0617)e^0.0617x. Plug in 6 for x and you'll get your Rate of Change of the Revenue at 6 years.