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19 December, 22:46

The population of goldfish in a marine farm is decreasing at the rate of 20 percent per year. The farm started with a goldfish population of 1,000. Part A

Create an equation that gives the number of goldfish in the nth year.

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  1. 19 December, 23:07
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    Step-by-step explanation:

    Part A:

    The equation modeling the problem is an exponential equation of the form:

    y = A (b) * ^ t

    Where,

    A: initial amount

    b: decrease rate

    t: time

    Substituting values we have:

    y = 1000 (0.80) ^ t

    Part B:

    For this case we substitute the value of y = 640 in the equation:

    640 = 1000 (0.80) ^ t

    We cleared t:

    640/1000 = (0.80) ^ t

    log0.80 ((0.80) ^ t) = log0.80 (640/1000)

    t = log0.80 (640/1000)

    t = 2 years
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