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22 November, 16:44

The number of bats in a colony is growing exponentially. After 2 years, there were 180 bats. After 5 years, there were 1440 bats. If the colony continues to grow at the same rate, how many bats are expected to be in the colony after 9 years? Do not include units in your answer.

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  1. 22 November, 16:57
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    23040 bats

    Explanation:

    Let N (t) be the number of bats at time t

    We know that exponential function

    y = ab^t

    According to question

    N (t) = ab^t

    Where t (in years)

    Substitute t=2 and N (2) = 180

    180 = ab^t ... (1)

    Substitute t=5 and N (5) = 1440

    1440 = ab^5 ... (2)

    Equation (1) divided by equation (2)

    180/1440 = ab^2 : ab^5

    1/8 = 1/b^3

    8 = 2^3

    Hence,

    1/2^3 = 1/b^3

    3/2 = 3/b

    Cross multiply

    3b = 2*3

    3b = 6

    b = 2

    Substitute the values of b in equation (1)

    180 = a (2) ^2

    180 = 4a

    a = 180/4

    a = 45

    Substitute t=9

    N (9) = 45 (2) ^9

    N = 45 * 512

    N = 23040

    Hence, after 9 years the expected bats in the colony=23040 bats
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