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A certain culture initially contains 10,000 bacteria and increase by 20% after every hour.

A) What will be the formula for numbers N(t) of bacteria after "t" hours?
B) How many bacteria are in culture at the end of 10 hours?

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Inam
2 answers

  1. Every hour, the amount is increased by 20%, meaning it's multiplied by 1.2

    So,

    N(t) = N(initial)*((1.2)^t)
    = 10000*((1.2)^t)
    So every hour the number gets multiplied with an additional 1.2

    When t = 10,

    N(10) = 10000*((1.2)^10)
    = 10000*6.191
    = 61,910

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    Arora

  2. Exponential Growth:

    N(t) = N ∙ ( 1 + r )ᵗ

    N = initial amount

    r = growth rate

    t = time elapsed

    In this case:

    N = 10,000

    r = 20% = 20 / 100 = 0.2

    A)

    N(t) = 10,000 ∙ ( 1 + 0.2 )ᵗ

    N(t) = 10,000 ∙ 1.2 ᵗ

    B)

    N(10) = 10,000 ∙ 1.2 ¹⁰ = 10,000 ∙ 1.2 ¹⁰ = 10,000 ∙ 6.1917364224 = 61,917.364224

    Approx.

    62,000

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    Bosnian

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