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Connally et al - Functions Modeling Change 5/e (Homework)

James Finch

Math - College, section 1, Fall 2019

Instructor: Dr. Friendly

Current Score : 0 / 39

Due : Sunday, January 27, 2030 00:00 EST

Last Saved : n/a Saving...  ()

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  • Instructions

    Functions Modeling Change, 5th edition, by Eric Connally, Deborah Hughes-Hallett, Andrew M. Gleason, et al., published by John Wiley & Sons, is designed to accomplish the main goals of the Precalculus course: to build a solid mathematical foundation and prepare students for Calculus. The authors achieve this by using real-world applications and focusing on a small number of key topics, thereby emphasizing depth of understanding rather than breadth of coverage. The WebAssign component of this text includes instant student feedback on randomized questions and reading links to a FlexPaper eBook.

    Question 1 includes the WebAssign graphing tool which allows the student to actively graph f(x) and the results from part (a).

    Question 2 is a multi-part question in which a real world situation is explored in detail. In part (a) the grading allows any equivalent form of the correct answer. In part (c) the student is asked to interpret information from the graph.

    Question 3 has randomized data given in the table so that each student receives different values.

    Question 4 presents the student with a randomized graph and grades the exponential decay function using special regression grading.

    Question 5 provides tolerance when grading the values in the formula to allow any correct answers after rounding.

    Question 6 uses simplified trigonometry grading to accept any correct formula using the sine function.

    Question 7 demonstrates trigonometry grading for a variety of functions.

    Question 8 has grading to enforce a simplified form per the directions.

    Question 9 uses list grading and displays the prompt given to indicate this to the student. Try entering the zeros in either order.

    Question 10 requires the student to enter a simplified rational expression. This demo assignment allows many submissions and allows you to try another version of the same question for practice wherever the problem has randomized values.

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1. –/5 points CHGFuncMod5 1.2.020. My Notes
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Let f(x) = 4 – x2.
(a) Compute each of the following expressions.
(i)
f(1) – f(0)
1 − 0
=
(ii)
f(2) – f(1)
2 − 1
=
(iii)
f(2) – f(0)
2 − 0
=

(b) Graph f(x). Illustrate each ratio in part (a) by sketching the line segment with the given slope.
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Over which interval is the average rate of decrease the greatest?
    

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2. –/13 points CHGFuncMod5 1.3.022. My Notes
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A small café sells drip coffee for $0.90 per cup. On average, it costs the café $0.20 to make a cup of coffee (for grounds, hot water, filters). The café also has a fixed daily cost of $200 (for rent, wages, utilities).
(a) Let R, C, and P be the café's daily revenue, costs, and profit, respectively, for selling x cups of coffee in a day. Find formulas for R, C, and P as functions of x. [Hint: The revenue, R, is the total amount of money that the café brings in. The cost, C, includes the fixed daily cost as well as the cost for all x cups of coffee sold. P is the café's profit after costs have been accounted for.]
R =
C =
P =

(b) Plot P against x.

For what x-values is the graph below the x-axis? (Round your answer to the nearest integer.)
    

For what x-values is the graph above the x-axis? (Round your answer to the nearest integer.)
    

Interpret your results.
When the graph of the profit function is above the x-axis, the café's profits are , meaning that it is money. When the graph of the profit function is below the x-axis, the café's profits are , meaning that it is money.

(c) Interpret the slope of your graph in practical terms.
    

Interpret the y-intercept of your graph in practical terms.
    

Interpret the x-intercept of your graph in practical terms.
    

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3. –/6 points CHGFuncMod5 1.R.005. My Notes
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The table below shows data for two populations (in hundreds) for five different years. Find the average rate of change per year of each population over the following intervals. (Give your answers correct to two decimal places.)
Year 1995 1997 2000 2005 2012
P1 49 59 69 79 89
P2 99 94 89 84 79
(a) 1995 to 2005
hundreds (P1)
hundreds (P2)

(b) 2000 to 2012
hundreds (P1)
hundreds (P2)

(c) 1995 to 2012
hundreds (P1)
hundreds (P2)

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4. –/3 points CHGFuncMod5 4.2.037. My Notes
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–/3
 
The figure below gives the voltage, V(t), across a circuit element at time t seconds. For t < 0, the voltage is a constant 70 volts; for t ≥ 0, the voltage decays exponentially.
WebAssign Plot
(a) Find a piecewise formula for V(t). (Round all numerical values to four decimal places.)
V(t) = 
   t < 0
   t ≥ 0

(b) At what value of t will the voltage reach 0.3? (Round your answer to three decimal places.)
t = s

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5. –/4 points CHGFuncMod5 4.R.033. My Notes
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–/4
 
Let P(t) be the population of a country, in millions, t years after 1990, with P(7) = 3.53 and P(13) = 3.93.
(a) Find a formula for P(t) assuming it is linear. (Round equation parameters to two decimal places.)
P(t) =


Describe in words the country's annual population growth given this assumption.

This answer has not been graded yet.



(b) Find a formula for P(t) assuming it is exponential. (Round equation parameters to three decimal places.)
P(t) =


Describe in words the country's annual population growth given this assumption.

This answer has not been graded yet.

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6. –/1 points CHGFuncMod5 7.5.027. My Notes
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–/1
 
Find a formula, using the sine function, for your height h above ground after t minutes on the Ferris wheel. Graph the function to check that it is correct.
A Ferris wheel is 47 meters in diameter and boarded at ground level. The wheel completes one full revolution every 9 minutes. At t = 0 you are in the three o'clock position and ascending.
h(t) =

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7. –/4 points CHGFuncMod5 7.R.075. My Notes
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For the function graphed below, find four possible formulas for the function:
WebAssign Plot
f1(x) = A cos(B(x − h)) + k, where A > 0.

f1(x) =


f2(x) = A cos(B(x − h)) + k, where A < 0.

f2(x) =


f3(x) = A sin(B(x − h)) + k, where A > 0.

f3(x) =


f4(x) = A sin(B(x − h)) + k, where A < 0.

f4(x) =

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8. –/1 points CHGFuncMod5 10.1.031. My Notes
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–/1
 
Find a simplified formula for g given that
f(x) = 
x + 2
x + 5
.
g(x) = f(h(x)) where h(x) = 5x2 − 2
g(x) =

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9. –/1 points CHGFuncMod5 11.R.023. My Notes
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–/1
 
Find the zeros of the function. (Enter your answers as a comma-separated list.)
y = 6x2 − 9x − 9
x =

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10. 0/1 points  |  Previous Answers CHGFuncMod5 11.SR.021. My Notes
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Perform the operation. Express the answer in reduced form.
3
12r + 5
+
5
48r 2 + 20r

120r+25+144r2
Incorrect: Your answer is incorrect. webMathematica generated answer key

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