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6 September, 12:41

A woman who has recovered from a serious illness begins a diet regimen designed to get her back to a healthy weight. She currently weighs 103 pounds. She hopes each week to multiply her weight by 1.08 each week. (a) Find a formula for an exponential function that gives the woman's weight w, in pounds, after t weeks on the regimen. (b) How long will it be before she reaches her normal weight of 135 pounds?

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  1. 6 September, 13:06
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    a.) w = 103 * 1.08^t

    b.) 3.5weeks

    Step-by-step explanation:

    If Her current weight is 103 pounds and she hopes to multiply her her weight each week by 1.08, then

    her weight after 1 week = 103 * 1.08 = 103 * 1.08¹

    Her weight after 2 weeks = [weight of week 1] * 1.08 = [103 * 1.08] * 1.08 = 103 * 1.08²

    Weight after 3 weeks = [weight of week 2] * 1.08 = [103 * 1.08 * 1.08] * 1.08 = 103 * 1.08³

    Hence weight (W) after t weeks = 103 * 1.08^t

    b.) If W = 135, Then

    103 * 1.08^t = 135

    1.08^t = 135/103

    1.08^t = 1.31

    Taking log of both sides,

    log 1.08^t = log 1.31

    t log 1.08 = log 1.32

    t = log 1.32/log 1.08

    t = 3.5 weeks.

    Hence, it will take her 3½ weeks to get to 135pounds weight.
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