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5 May, 21:35

A population of deer increases at a rate of 4% annually. If the starting population is 800 deer, how long will it take for the population to grow to 1,200? Round your answer to the nearest tenth of a year.

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  1. 5 May, 22:02
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    Answer: 10.4 years

    Step-by-step explanation:

    A deer population grows at a rate of 4% annually. The growth rate is exponential. We would apply the formula for exponential growth which is expressed as

    y = b (1 + r) ^ t

    Where

    y represents the population after t years.

    t represents the number of years.

    b represents the initial population.

    r represents rate of growth.

    From the information given,

    b = 800

    r = 4% = 4/100 = 0.04

    y = 1200

    Therefore

    1200 = 800 (1 + 0.04) ^t

    1200/800 = (1.04) ^t

    1.5 = (1.04) ^t

    Taking log of both sides to base 10

    Log 1.5 = log1.04^t = tlog1.04

    0.1761 = t * 0.017

    t = 0.1761/0.017

    t = 10.4 years
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