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# Help with Calculus question, Integrals?

I'm not really sure what is being asked and can't find my answer through textbook. If you could show how you got the answer I would appreciate it.

The rate of change for a chemical process is f'(t) = e^.025t. At t = 0 there were 40 grams of the substance. Write the function that gives the amount of material present at any time t.

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- AshLv 72 months ago
f'(t) = e⁰·⁰²⁵ᵗ

f(t) = ∫f'(t) dt = ∫e⁰·⁰²⁵ᵗ dt

f(t) = (e⁰·⁰²⁵ᵗ)/0.025 + C

Given f(0) = 40

f(0) = (e⁰)/0.025 + C

40 = 1/0.025 + C

40 = 40 + C

C = 0

f(t) = (e⁰·⁰²⁵ᵗ)/0.025

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- VamanLv 72 months ago
f'(t) = e^.025t. At t = 0 there were 40 grams.

Integrate it. You get

f(t)= 1/(0.0251) exp(0.0251 t)+c

at t=0. f(0)=40

f(t) = 40 + 1/(0.0251) exp(0.0251 t)

It increases with time.

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- 2 months ago
Is f'(t) the same as the derivative of the function?

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