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tmax8437
03.03.2020 •
Mathematics
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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Ответ:
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.
Ответ:
y1 being the y coordinate
x1 being the x coordinate
m being the gradient (or slope)
y - 3 = 5 (x - - 4)
y - 3 = 5x + 20
y = 5x + 23