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Chapter 0: Problem 108

(a) The amount in your savings account is a function of your salary. (b) The speed at which a free-falling baseball strikes the ground is a function of the height from which it was dropped.

Short Answer

Expert verified
For both parts, (a) and (b), the relationships described can be considered functions. In (a), the amount in the savings account is a function of salary. In (b), the speed at which a free-falling baseball hits the ground is a function of the height from which it was dropped.

Step by step solution

01

Understanding Part (a)

Consider the relationship between salary (input) and the amount in a savings account (output). For every salary value, there is likely to be a corresponding savings amount, and each salary level should ideally relate to one savings amount. Therefore, the amount in the savings account can be regarded as a function of salary.
02

Understanding Part (b)

Consider the relationship between the height of a free-falling baseball's drop (input) and the speed at which it hits the ground (output). According to the physics law of free fall, for any given height, there is a corresponding speed that the falling ball will reach. Therefore, the speed at which the ball hits the ground can be viewed as a function of the height from which it was dropped.

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Most popular questions from this chapter

In Exercises 39-54, (a) find the inverse function of \(f\), (b) graph both \(f\) and \(f^{-1}\) on the same set of coordinate axes, (c) describe the relationship between the graphs of \(f\) and \(f^{-1}\), and (d) state the domain and range of \(f\) and \(f^{-1}\). $$ f(x)=3 x+1 $$

Path of a Ball The height \(y\) (in feet) of a baseball thrown by a child is $$ y=-\frac{1}{10} x^{2}+3 x+6 $$ where \(x\) is the horizontal distance (in feet) from where the ball was thrown. Will the ball fly over the head of another child 30 feet away trying to catch the ball? (Assume that the child who is trying to catch the ball holds a baseball glove at a height of 5 feet.)

(a) use the position equation \(s=-16 t^{2}+v_{0} t+s_{0}\) to write a function that represents the situation, (b) use a graphing utility to graph the function, (c) find the average rate of change of the function from \(t_{1}\) to \(t_{2}\), (d) interpret your answer to part (c) in the context of the problem, (e) find the equation of the secant line through \(t_{1}\) and \(t_{2}\), and (f) graph the secant line in the same viewing window as your position function. An object is dropped from a height of 80 feet. $$ t_{1}=1, t_{2}=2 $$

Average Price The average prices \(p\) (in thousands of dollars) of a new mobile home in the United States from 1990 to 2002 (see figure) can be approximated by the model $$ p(t)= \begin{cases}0.182 t^{2}+0.57 t+27.3, & 0 \leq t \leq 7 \\ 2.50 t+21.3, & 8 \leq t \leq 12\end{cases} $$ where \(t\) represents the year, with \(t=0\) corresponding to 1990. Use this model to find the average price of a mobile home in each year from 1990 to 2002 . (Source: U.S. Census Bureau)

In Exercises 39-54, (a) find the inverse function of \(f\), (b) graph both \(f\) and \(f^{-1}\) on the same set of coordinate axes, (c) describe the relationship between the graphs of \(f\) and \(f^{-1}\), and (d) state the domain and range of \(f\) and \(f^{-1}\). $$ f(x)=x^{3 / 5} $$
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