Retail revenue each year from Internet shopping is approximated by the function , where is measured in billions of dollars and is measured in years, with corresponding to the beginning of 1997.
How fast was the retail revenue/year from Internet shopping changing at the beginning of the year 2000?

A) $4.385 billion/yr
B) $4.315 billion/yr
C) $11.625 billion/yr
D) $4.865 billion/yr

Question

Retail revenue each year from Internet shopping is approximated by the function   , where  is measured in billions of dollars and  is measured in years, with  corresponding to the beginning of 1997. ​
How fast was the retail revenue/year from Internet shopping changing at the beginning of the year 2000?
​
A) $4.385 billion/yr 
B) $4.315 billion/yr 
C) $11.625 billion/yr 
D) $4.865 billion/yr

Quizplus · Accepted Answer

We need to find the derivative of the given function with respect to time (in years), evaluated at t=3 (since the beginning of 2000 is 3 years after the beginning of 1997). 
Taking the derivative of the function with respect to t, we get: 
f'(t) = (11/6) e^(0.035t) 
Evaluating this at t=3, we get: 
f'(3) = (11/6) e^(0.035*3) 
f'(3) ≈ 4.865 billion/yr 
Therefore, the answer is D.

Retail Revenue Each Year from Internet Shopping Is Approximated by the Function