Ask questions and get helpful answers.

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?

  1. 👍
  2. 👎
  3. 👁
  4. ℹ️
  5. 🚩
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

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩
  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

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩

Answer this Question

Related Questions

Still need help?

You can ask a new question or browse existing questions.