Revenue of Sand Blasting Bolts

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Lesson Parent: 
Differentiation V: Derivatives and Rates of Change
Problem: 

The annual revenue for sand blasting bolts over the last ten years can be approximated by R(t)=0.91t4−37.5t3+560t2−2785t+8156 where t=0 is ten years ago and t=10 is today. At what rate was the revenue increasing three years ago?

Answer: 

$791.02 per year

SAMPLE SOLUTION

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Solution: 

The problem explicitly asks for the rate of change of revenue. We first need to determine R′(t). We know that R(t) is a polynomial and that the derivative of a polynomial is easily determined. Therefore,

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From the definition of t defined in the problem, we know that three years ago is t=7. Therefore, the rate of revenue increase three years ago is <Sign in to see all the formulas>. So the revenue was increasing by $791.02 per year three years ago.