Please help!!!! I just need help with part c. A pumpkin is being grown for a contest at the state fair. Its growth can be modeled

Question

Please help!!!! I just need help with part c.

A pumpkin is being grown for a contest at the state fair. Its growth can be modeled by the equation P=25(1.56)^n, where P is the weight of the pumpkin in pounds and n is the number of weeks the pumpkin has been growing.

a. By what percentage does the pumpkin grow every week?
(my answer) The pumpkin grows 156% percent every week.

b. After how many weeks will the pumpkin be 80 pounds?
(my answer)The pumpkin will be 80 pounds after 3 weeks.

c. What if the growth percentage changed to 32, after how many weeks will the pumpkin be 80 pounds?

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Answers ( No )

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    2021-11-23T20:29:34+00:00

    A) the growth is 56% per week. The 1.56 is multiplying the weight of the pumpkin now by the 56% to get the total weight after the 56% increase.

    B) Replace P with 80 and solve for n:

    80 = 25(1.56)^n

    Divide each side by 25:

    80/25 = 1.56^n / 25

    3.2 = 1.56^n

    Take the natural logarithm of both sides:

    ln(3.2) = ln(1.56^n)

    Remove the exponent:

    ln(3.2) = n(ln(1.56)

    Divide both sides by ln(1.56)

    n = ln(3.2) / ln(1.56)

    n = 2.6 weeks, round to 3 weeks.

    C)  Change 1.56 to 1.32 and redo the same calculation from B.

    80 = 25(1.32)^n

    80/25 = 1.32^n /25

    3.2 = 1.32^n

    ln(3.2) = ln(1.32^n)

    ln(3.2) = n(ln(1.32)

    n = ln(3.2) / ln(132)

    n = 4.2, round to 4 weeks.

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