The population of watesville decreases at a rate of 1.6% each year if the population was 62,500 in 2015 what will it be in 2021

Question

The population of watesville decreases at a rate of 1.6% each year if the population was 62,500 in 2015 what will it be in 2021

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RuslanHeatt 3 years 2021-07-31T05:16:01+00:00 1 Answers 68 views 0

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  1. King
    0
    2021-07-31T05:17:32+00:00
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    Answer:

    Step-by-step explanation:

    We need to first find the model for this particular situation, knowing that this is an exponential decay problem. The main equation for exponential growth/decay (as far as population goes for our problem) is

    y=a(b)^x where a is the initial population, b is the rate of decrease in the population which can also be written as (1 – r), y is the population after a certain amount of time, x, goes by. We will let year 2015 = 0 so year 2021 can = 6. This keeps our numbers lower and doesn’t change the answer!

    Our initial population in the year x = 0 is 62500. Our rate of decay is

    (1 – .016) so our b value is .984

    Filling in to find our model:

    y=62500(.984)^x

    Now we can use that model and sub in a 6 for x to find the population in the year 2021:

    y=62500(.984)^6 and

    y = 62500(.9077590568) so

    y = 56734.9 or, rounded to the nearest person, 56735

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