Homework Assignment 2 (2 Pts Each)

Question

Name: Class: Date: Homework Assignment 2 (2pts each) Enter 1. What was the average rate of change of sales between 1989 and 1999? __________ CD players/year 2. Determine the average rate of change of the function f(x) = x³ - 5x² between x = 0 and x = 10. 3. Use the given graphs of f and g to evaluate the expression. __________ 4. Use and to evaluate the expression. __________ 5. Determine the average rate of change of the function f(x) = 9 - 7x between x = 2 and x = 3. 6. Use the given graphs of f and g to evaluate the expression. __________ 7. Use the given graphs of f and g to evaluate the expression. __________ 8. A man is running around a circular track 200 m in circumference. What was the man's average speed (rate) between 70 s and 164 s? __________ m/s 9. Determine the average rate of change of the function f(x) = x + x⁴ between x = 0 and x = 2. 10. Determine the average rate of change of the function f(t) = t² - 4t between t = -5 and t = -4.

Dr. Jack HW Helper · Accepted Answer

The following assignment addresses calculations related to the average rate of change and other evaluations based on functions and real-world scenarios. 1. Average Rate of Change of CD Sales (1989-1999) The average rate of change of CD players sold from 1989 to 1999 can be calculated using the formula for average rate of change: Average Rate of Change = (f(b) - f(a)) / (b - a) Let’s denote: a = 1989 b = 1999 f(1989) = x f(1999) = y The average rate of change then is: (y - x) / (1999 - 1989) = (y - x) / 10 Replace x and y with specific sales data (not provided here) to finalize the average rate of change. 2. Average Rate of Change for f(x) = x³ - 5x² (from 0 to 10) We find: f(0) = 0³ - 5(0)² = 0 f(10) = 10³ - 5(10)² = 1000 - 500 = 500 Using the average rate of change formula: Average Rate of Change = (f(10) - f(0)) / (10 - 0) = (500 - 0) / 10 = 50 3. Evaluation using Graphs of f and g This step requires the specific graphical details of functions f and g, which are not provided in the assignment. Typically, one would identify values from the graphs at the necessary points. Solution: Evaluating would lead to a specific outcome depending on the graph locations. 4. Evaluation of an Expression Similar to the above, this would require knowing values or functions to evaluate the specified expression. Solution: Substitute known values as per the graphs given for functions f and g. 5. Average Rate of Change for f(x) = 9 - 7x (from 2 to 3) Calculating: f(2) = 9 - 7(2) = 9 - 14 = -5 f(3) = 9 - 7(3) = 9 - 21 = -12 So, Average Rate of Change = (-12 - (-5)) / (3 - 2) = (-12 + 5) / 1 = -7 6-7. Evaluating Expressions using Graphs of f and g As with sections 3 and 4, the evaluations depend on the positions represented on the graphs, needing analysis. 8. Average Speed Around a Circular Track Distance = 200 m; for average speed between 70 s and 164 s, we first need the distance covered in that time. Let’s denote distance covered as d. Using the stopwatch observations, we calculate tot

Homework Assignment 2 (2 Pts Each) ✓ Solved

Name: Class: Date: Homework Assignment 2 (2pts each) Enter

Paper For Above Instructions

1. Average Rate of Change of CD Sales (1989-1999)

2. Average Rate of Change for f(x) = x³ - 5x² (from 0 to 10)

3. Evaluation using Graphs of f and g

4. Evaluation of an Expression

5. Average Rate of Change for f(x) = 9 - 7x (from 2 to 3)

6-7. Evaluating Expressions using Graphs of f and g

8. Average Speed Around a Circular Track

9. Average Rate of Change for f(x) = x + x⁴ (from 0 to 2)

10. Average Rate of Change for f(t) = t² - 4t (from -5 to -4)

References