Anonymous
Anonymous asked in Education & ReferenceHomework Help · 2 months ago

calc help?

The birth rate of a population is

b(t) = 2300e0.021t   people per year and the death rate is  d(t)= 1490e0.015t 

 people per year, find the area between these curves for 0 ≤ t ≤ 10. (Round your answer to the nearest integer.)

1 Answer

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  • 2 months ago

    Area under b(t) = births

    ∫ 2300e^(.021t) = (2300/.021)e^(.021t)

     

    ∫₀¹⁰ 2300e^(.021t) = (2300/.021)e^(.021 * 10) -  (2300/.021)e^(.021 * 0)

    ∫₀¹⁰ 2300e^(.021t) =  135,117 - 109,524

    ∫₀¹⁰ 2300e^(.021t) = 25,593

    -------------------------

    Area under d(t) = deaths

    ∫ 1490e^(.015t) = (1490/.015)e^(.015t)

    ∫₀¹⁰ 1490e^(.015t) = (1490/.015)e^(.015 * 10) - (1490/.015)e^(.015 * 0)

    ∫₀¹⁰ 1490e^(.015t) = 115,409 - 99,333

    ∫₀¹⁰ 1490e^(.015t)  = 16,076

    -----------------------

    Area between curves

    births  - deaths

    a = 25,593 - 16,076

    a = 9,517 <––––––

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