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21 November, 06:49

The number of birds in a forest is decreasing by 3% every year. In 2000 there were 5,400 birds. Write an equation that represents the number, y, of birds x years after 2000. How many birds will there be in 2025? Round your answer to the nearest whole number.

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  1. 21 November, 10:34
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    Step-by-step explanation:

    This is a Compound interest problem with a decreasing rate. It is given by the formula:

    A = P (1 + / - R) ^T

    Where A = amount after time T

    P = principal or initial amount

    R = rate of increase or decrease

    T = time elapsed

    There's + / - because + is used in the case when the amount is increasing at a particular rate and - is used whe the amiunt is decreasing.

    In 2000 there were 5,400 birds and the number of birds is decreasing by 3% (0.03) every year.

    The number of birds, y, that will be there x years after 2000 will be:

    y = 5400 (1 - 0.03) ˣ

    2025 is 25 years ahead of 2000, so x = 25

    Therefore, the number of birds in 2025 will be:

    y = 5400 (1 - 0.03) ^25

    y = 5400 (0.97) ^25

    y = 5400 * 0.467

    y = 2522 birds

    There will be 2522 birds in 2025.
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