# Derivatives, Rate of Change and the Fundamental Theorem of Calculus

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1. The resale value of a certain industrial machine decreases at a rate that depends on its age. When the machine is t years old, the rate at which its value is changing is -960e^-t/5 dollars per year.

a) Express the value of the machine in terms of its age and initial value.

b) If the machine was originally worth $5,200, how much will it be worth when it is 10 years old

2. Evaluate the following integral using the fundamental theorem of calculus.

Integrate with limits 1 to 9 (t^1/2 -4 /t^1/2) dt

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Derivatives, Rate of Change and the Fundamental Theorem of Calculus are investigated. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question.

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