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 $R(t)=0.91t^4-37.5t^3+560t^2-2785t+8156$ 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

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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.