Antonio, a professional wrestler, went on a very strict liquid diet for 26 weeks to lose weight. When he began the diet, he weighed in at a healthy 235 pounds and during the diet, he consistently lost 1.5% of his body weight each week. His weight loss can be modeled by the function [tex]W(t) = 235(0.985)^t[/tex], where [tex]W[/tex] is his weight in pounds and [tex]t[/tex] is the time in weeks that he has been on the diet.

1. What was his weight in pounds after 5 weeks?
2. How long did it take (in weeks) for him to weigh 161.05 pounds?

Question

13-09-2023
Mathematics

High School

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Antonio, a professional wrestler, went on a very strict liquid diet for 26 weeks to lose weight. When he began the diet, he weighed in at a healthy 235 pounds and during the diet, he consistently lost 1.5% of his body weight each week. His weight loss can be modeled by the function [tex]W(t) = 235(0.985)^t[/tex], where [tex]W[/tex] is his weight in pounds and [tex]t[/tex] is the time in weeks that he has been on the diet.

1. What was his weight in pounds after 5 weeks?
2. How long did it take (in weeks) for him to weigh 161.05 pounds?

Answer :

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Qwbox Qwbox · Answer 1 · 2024-01-18T23:49:36-05:00

Antonio's weight after 5 weeks was 202.34 pounds, and it took him 19 weeks to weigh in at 161.05 pounds.

To find Antonio's weight after 5 weeks, we can simply substitute t = 5 into the given exponential function:

W(5) = 235(0.985)⁵

W(5) ≈ 209.88 pounds

So his weight after 5 weeks was approximately 209.88 pounds. To find how long it took him to weigh in at 161.05 pounds, we can set the function equal to 161.05 and solve for t:

161.05 = 235(0.985)ᵗ

0.685106383 ≈ 0.985ᵗ

t ≈ 25.5 weeks

So it took him approximately 25.5 weeks to weigh in at 161.05 pounds

To know more about exponential function, visit,

https://brainly.com/question/2456547

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Complete question - Antonio, a professional wrestler, went on a very strict liquid diet for 26 weeks to lose weight. When he began the diet, he weighed in at a healthy 235 pounds and during the diet, he consistently lost 1. 5% of his body weight each week. His weight loss can be modeled by the function W (t) = 235(0. 985)ᵗ where W is his weight in pounds and t is the time in weeks that he has been on the diet. What was his weight in pounds after 5 weeks? How long did it take(in weeks) him to weigh in at 161. 05 pounds?