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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  • Ash
    Lv 7
    8 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

  • Mangal
    Lv 4
    8 months ago

    see image ... ... ... 

    Attachment image
  • Vaman
    Lv 7
    8 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.

  • 8 months ago

    Is f'(t) the same as the derivative of the function?

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