9. Income-Education Sociologists studied the relation between income and number of years of education for members of a particular urban group. They found that a person with x years of education before seeking regular employment can expect to receive an average yearly income of y dollars per year, where y = 5x/2 + 5900 4 < x < 16 Find the rate of change of income with respect to number of years of education. Evaluation the expression when x 9.
9. Income-Education Sociologists studied the relation between income and number of years of education for members of a particular urban group. They found that a person with x years of education before seeking regular employment can expect to receive an average yearly income of y dollars per year, where y = 5x/2 + 5900 4 < x < 16 Find the rate of change of income with respect to number of years of education. Evaluation the expression when x 9.
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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#9,#11
![### Calculus Problems
#### Motion Problems:
1. **Given:**
- \( s = 2t^2 - 4 \) over the interval \([7, 7.5]\); \( t = 7 \)
2. **Given:**
- \( s = \frac{1}{2} t + 1 \); \([2, 2.1]\); \( t = 2 \)
3. **Given:**
- \( s = 5t^3 + 3t + 24 \); \([1, 1.01]\); \( t = 1 \)
4. **Given:**
- \( s = -3t^2 + 2t + 1 \); \([1, 1.25]\); \( t = 1 \)
5. **Given:**
- \( s = t^4 - 2t^3 + t \); \([2, 2.1]\); \( t = 2 \)
6. **Given:**
- \( s = 3t^4 - t^{7/2} \); \([0, \frac{1}{4}]\); \( t = 0 \)
#### Economic Application:
9. **Income–Education Relationship:**
- Formula: \( y = 5x^{5/2} + 5900 \)
- Range: \( 4 \leq x \leq 16 \)
- Task: Find the rate of change of income with respect to education years for \( x = 9 \).
#### Physics Application:
10. **Volume of a Sphere:**
- Formula: \( V(r) = \frac{4}{3} \pi r^3 \)
- Given radius: \( r = 1.5 \, \text{m} \)
- Task: Find the rate of change with respect to the radius.
#### Biology Application:
11. **Skin Temperature:**
- Formula: \( T = 32.8 + 0.27(T_e - 20) \)
- Task: Determine the rate of change of \( T \) with respect to \( T_e \).
12. **Cell Volume:**
- Formula: \( V = \frac{3}{4} \pi r^3 \)
- Given: \( r](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0e2d6f28-e3d7-414c-b1d4-a752131175c2%2F369bf9b1-0cd3-4623-a2de-de6f475726e2%2Fxwtgpl6.jpeg&w=3840&q=75)
Transcribed Image Text:### Calculus Problems
#### Motion Problems:
1. **Given:**
- \( s = 2t^2 - 4 \) over the interval \([7, 7.5]\); \( t = 7 \)
2. **Given:**
- \( s = \frac{1}{2} t + 1 \); \([2, 2.1]\); \( t = 2 \)
3. **Given:**
- \( s = 5t^3 + 3t + 24 \); \([1, 1.01]\); \( t = 1 \)
4. **Given:**
- \( s = -3t^2 + 2t + 1 \); \([1, 1.25]\); \( t = 1 \)
5. **Given:**
- \( s = t^4 - 2t^3 + t \); \([2, 2.1]\); \( t = 2 \)
6. **Given:**
- \( s = 3t^4 - t^{7/2} \); \([0, \frac{1}{4}]\); \( t = 0 \)
#### Economic Application:
9. **Income–Education Relationship:**
- Formula: \( y = 5x^{5/2} + 5900 \)
- Range: \( 4 \leq x \leq 16 \)
- Task: Find the rate of change of income with respect to education years for \( x = 9 \).
#### Physics Application:
10. **Volume of a Sphere:**
- Formula: \( V(r) = \frac{4}{3} \pi r^3 \)
- Given radius: \( r = 1.5 \, \text{m} \)
- Task: Find the rate of change with respect to the radius.
#### Biology Application:
11. **Skin Temperature:**
- Formula: \( T = 32.8 + 0.27(T_e - 20) \)
- Task: Determine the rate of change of \( T \) with respect to \( T_e \).
12. **Cell Volume:**
- Formula: \( V = \frac{3}{4} \pi r^3 \)
- Given: \( r
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