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enot [183]
2 years ago
11

A woman who has recovered from a serious illness begins a diet regimen designed to get her back to a healthy weight. She current

ly 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?
Mathematics
1 answer:
WINSTONCH [101]2 years ago
7 0

Answer:

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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The volume of the cake is 1470 in³. 
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we know the diameter of the cylinder is 12 in. and the radius is half of the diameter. 
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Now that we know the height of the cylinder is about 13 in., we know the height of the cone, because the problem says that the height of the cone is half the height of the cylinder. 
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volume of the cone = (3.14)(6²)(6.5 ÷ 3)
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6 0
3 years ago
2, 6, 10, 15, ...<br><br> O Arithmetic<br> O Geometric<br> O Neither<br> 
natima [27]

Given:

The sequence is:

2, 6, 10, 15,...

To find:

Whether the given sequence is Arithmetic, Geometric, Neither.

Solution:

We have,

2, 6, 10, 15,...

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Since 4\neq 5, therefore the given sequence has no common difference. It means it is not an arithmetic sequence.

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Since 3\neq \dfrac{5}{3}, therefore the given sequence has no common ratio. It means it is not a geometric sequence.

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