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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
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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### 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
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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