A hippopotamus’s typical growth rate is typically 50.5% per year when considering it’s weight in pounds from birth to maturity. Using the co

Question

A hippopotamus’s typical growth rate is typically 50.5% per year when considering it’s weight in pounds from birth to maturity. Using the continuous growth equation, how long would it take a 70lb infant hippo to reach an average adult weight of 3100lbs?

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Lyla 4 weeks 2021-12-27T07:19:39+00:00 1 Answer 0 views 0

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    2021-12-27T07:21:12+00:00

    Answer:

    9.3 years

    Step-by-step explanation:

    we know that

    The equation of a exponential growth is equal to

    y=a(1+r)^x

    where

    y is the weight in pounds

    x is the number of years

    a is the initial value or y-intercept

    we have

    a=70\ lb\\r=50.5\%=50.5\100=0.505

    substitute

    y=70(1+0.505)^x

    y=70(1.505)^x

    For y=3,100 lb

    substitute in the equation

    3,100=70(1.505)^x

    solve for x

    \frac{310}{7} =(1.505)^x

    apply log both sides

    log(\frac{310}{7}) =log[(1.505)^x]

    log(\frac{310}{7}) =(x)log(1.505)

    x=log(\frac{310}{7})/log(1.505)=9.3\ years

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