31-32 - Linear Functions Given Numerically A table of valuesfor a linear function f is given. (a) Find the rate of change of f.(b) Express f in the form f(x) = ax + b31.32.f(x)f(x)311104132-4- 13- 196.1658197

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Answered: 31-32 - Linear Functions Given…

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter2: Functions

Section2.5: Linear Functions And Models

Problem 31E

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Maximum Sales Growth This is a continuation of Exercise 10. In this exercise, we determine how the sales level that gives the maximum growth rate is related to the limit on sales. Assume, as above, that the constant of proportionality is 0.3, but now suppose that sales grow to a level of 4 thousand dollars in the limit. a. Write an equation that shows the proportionality relation for G. b. On the basis of the equation from part a, make a graph of G as a function of s. c. At what sales level is the growth rate as large as possible? d. Replace the limit of 4 thousand dollars with another number, and find at what sales level the growth rate is as large as possible. What is the relationship between the limit and the sales level that gives the largest growth rate? Does this relationship change if the proportionality constant is changed? e. Use your answers in part d to explain how to determine the limit if we are given sales data showing the sales up to a point where the growth rate begins to decrease.
Average Rate of change A fucntion f is given. (a) Find the average rate of change of f between x=0 and x=0 ,and the average rate of change of f between x=15 and x=50 . (b) Were the two average rates of change that you found in part (a) the same? (c) Is the function linear? If so, what is its rate of change? f(x)=12x6
Average Rate of change A fucntion f is given. (a) Find the average rate of change of f between x=0 and x=0 , and the average rate of change of f between x=15 and x=50 .(b) Were the two average rates of change that you found in part (a) the same? (c) Is the function linear? If so, what is its rate of change? f(x)=83x
Linear Functions A linear functions is described either verbally, numerically, or graphically. Express f in the form f(x)=ax+b . The function has rate of change —2 and initial value 3.

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31-32 - Linear Functions Given Numerically A table of values for a linear function f is given. (a) Find the rate of change of f. (b) Express f in the form f(x) = ax + b 31. 32. f(x) f(x) 3 11 10 4 13 2 -4 - 13 - 19 6. 16 5 8 19 7