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A 25-year old woman burns 300 - 20t cal/hr while walking on her treadmill. Her caloric intake from drinking Gatorade is 140t calories during the tth hour. What is her net decrease in calories after walking for 4 hours? calories burned

A 25-year old woman burns 300 - 20t cal/hr while walking on her treadmill. Her caloric intake from drinking Gatorade is 140t calories during the tth hour. What is her net decrease in calories after walking for 4 hours? calories burned

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Problem Statement:** A 25-year-old woman burns calories at a rate given by the formula \(300 - 20t\) calories per hour (\(\text{cal/hr}\)) while walking on her treadmill. Additionally, she consumes calories by drinking Gatorade at a rate of \(140t\) calories during the \(t\)-th hour. The goal is to determine her net decrease in calories after walking for 4 hours. **Task:** Calculate the net decrease in calories after 4 hours of walking. **Diagrams/Graphs:** There are no diagrams or graphs in the image. **Solution Approach:** 1. **Calories Burned:** Calculate the total calories burned over 4 hours using the formula \(300 - 20t\): - For \(t=1\): \(300 - 20(1) = 280\) cal - For \(t=2\): \(300 - 20(2) = 260\) cal - For \(t=3\): \(300 - 20(3) = 240\) cal - For \(t=4\): \(300 - 20(4) = 220\) cal Total calories burned = \(280 + 260 + 240 + 220 = 1000\) cal 2. **Calories Consumed:** Calculate the calories consumed by drinking Gatorade over 4 hours using the formula \(140t\): - For \(t=1\): \(140(1) = 140\) cal - For \(t=2\): \(140(2) = 280\) cal - For \(t=3\): \(140(3) = 420\) cal - For \(t=4\): \(140(4) = 560\) cal Total calories consumed = \(140 + 280 + 420 + 560 = 1400\) cal 3. **Net Decrease in Calories:** Net decrease = Total calories burned - Total calories consumed Net decrease = \(1000 - 1400 = -400\) cal Therefore, after 4 hours of walking, her net decrease in calories is \(-400\) calories, indicating a net increase in calorie consumption.
Transcribed Image Text:**Problem Statement:** A 25-year-old woman burns calories at a rate given by the formula \(300 - 20t\) calories per hour (\(\text{cal/hr}\)) while walking on her treadmill. Additionally, she consumes calories by drinking Gatorade at a rate of \(140t\) calories during the \(t\)-th hour. The goal is to determine her net decrease in calories after walking for 4 hours. **Task:** Calculate the net decrease in calories after 4 hours of walking. **Diagrams/Graphs:** There are no diagrams or graphs in the image. **Solution Approach:** 1. **Calories Burned:** Calculate the total calories burned over 4 hours using the formula \(300 - 20t\): - For \(t=1\): \(300 - 20(1) = 280\) cal - For \(t=2\): \(300 - 20(2) = 260\) cal - For \(t=3\): \(300 - 20(3) = 240\) cal - For \(t=4\): \(300 - 20(4) = 220\) cal Total calories burned = \(280 + 260 + 240 + 220 = 1000\) cal 2. **Calories Consumed:** Calculate the calories consumed by drinking Gatorade over 4 hours using the formula \(140t\): - For \(t=1\): \(140(1) = 140\) cal - For \(t=2\): \(140(2) = 280\) cal - For \(t=3\): \(140(3) = 420\) cal - For \(t=4\): \(140(4) = 560\) cal Total calories consumed = \(140 + 280 + 420 + 560 = 1400\) cal 3. **Net Decrease in Calories:** Net decrease = Total calories burned - Total calories consumed Net decrease = \(1000 - 1400 = -400\) cal Therefore, after 4 hours of walking, her net decrease in calories is \(-400\) calories, indicating a net increase in calorie consumption.
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