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16 July, 12:13

The number of bacteria in culture grows 80% each hour. Suppose. There are 250 bacteria in the original culture.

a. Write an exponential growth model showing the number of bacteria after x hours.

b. Calculate the number of bacteria after 10 hours.

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  1. 16 July, 16:12
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    Answer: (a) y = 250 (1.8) ˣ (b) 89,262 bacteria

    Step-by-step explanation:

    Use the exponential growth formula y = a (b) ˣ where

    a = Initial Value b = 1 + r (for growth) or 1 - r for decay r = rate (convert percent to a decimal)

    a) Given: a = 250, r = 80% (.80) → b = 1.8

    y = 250 (1.8) ˣ

    b) Given: x = 10

    y = 250 (1.8) ¹⁰

    y = 89,261.68 = 89,262 (rounded to the nearest whole number)
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