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?

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.