Math Problem Statement
Solution
Let's go through the questions visible in the image you uploaded.
The problem involves the function , where represents weight in pounds, and represents the number of calories consumed by the subject in a day.
Here's a breakdown of each part:
(a) In the statement
- The function means the weight of a subject when they consume 1900 calories is 160 pounds.
- The units of 1900 are calories (cal).
- The units of 160 are pounds (lb).
(b) In the statement
- The units of 2000 are also calories (cal), as it's a daily calorie intake.
- The units of 165 are pounds (lb), as this refers to the weight of the subject.
(c) In the statement
- This inverse function means that if the subject's weight is 169 pounds, the subject is consuming 2200 calories per day.
- The units of 169 are pounds (lb), as this is the weight.
- The units of 2200 are calories (cal).
(d) What are the units of ?
- represents the rate of change of weight with respect to calories consumed.
- The units of are pounds per calorie (lb/cal).
(e) If Sam increases her calorie intake from 2600 to 2620 calories, her weight will increase by approximately 0.2 pounds.
- Here you need to find .
- The weight change per calorie is , so .
- Solving for , you get:
This fills the blank for , which is 0.01 lb/cal.
Would you like further details on any part or have any other questions?
Five Related Questions:
- How is the derivative interpreted in terms of weight change with calorie intake?
- What would the weight change be if Sam increased her intake from 2500 to 2600 calories?
- Can we determine Sam’s weight if she consumes 1900 calories a day based on this model?
- What does tell us about a person's calorie intake if we know their weight?
- How would the interpretation change if we used a different measurement unit for weight (e.g., kilograms)?
Tip:
When interpreting inverse functions like , remember they reverse the input-output relationship, letting you find inputs from known outputs.
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Math Problem Analysis
Mathematical Concepts
Functions
Derivatives
Inverse Functions
Formulas
f(1900) = 160
f(2000) = 165
f^{-1}(169) = 2200
f'(c) = dW/dc
f'(2600) = 0.01 lb/cal
Theorems
Derivative of a function
Inverse function theorem
Suitable Grade Level
Grades 11-12
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