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

Question

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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Ivy 1 month 2021-10-14T01:11:20+00:00 1 Answer 0 views 0

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    2021-10-14T01:12:45+00:00

    Answer:

    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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