ACTIVITY 1.9 FUND-RAISER REVISITED

g. Solve the equation in part e using a graphical approach.

83

SUMMARY Activity 1.9 ^ 1. To solve an equation using a numerical approach, use a guess, check, and repeat

process. 2. To solve an equation using a graphical approach, read the appropriate coordinates

on the graph of the equation relating x and y. 3. A solution of an equation containing one variable is a replacement value for the

variable that produces equal values on both sides of the equation. 4. A graph is said to be continuous, if you can place your pencil on any point on the

graph and then trace the entire graph without lifting the pencil off the paper. The graph has no breaks or holes.

EXERCISES! Activity 1.9 J 1. Your local gas station is having a super sale and is selling regular unleaded gasoline

for three hours at $1,239 per gallon. a. Let X be the independent variable representing the number of gallons purchased.

Let f be the dependent variable representing the total cost of the fuel. Write an equation relating x and C.

b. What is the practical domain for xl

c. Use the equation from part a to complete the following table. X, N U M B E R O F G A L L O N S P U R C H A S E D 5 10 15 20

c, T O T A L C O S T O F T H E P U R C H A S E

84 CHAPTER 1 INTRODUCTION TO PROBLEM SOLVING AND MATHEMATICAL MODELS

d. You have only $10 with you. Use the equation from part a to write an equation that can be used to determine how many gallons you can purchase.

e. Solve your equation from part d using a numerical approach.

f. The graph of the equation determined in part a is given below. Use the graph to estimate the number of gallons you can purchase with $10.

26 24 22 20 18 16 14

r 12 S 10

8 6 4 2

,y

5 10 15 Number of Gallons Purchased

20

2. You are president of the high school band booster club. You have arranged for the school's jazz band to perform at a local coffee shop for three hours. In exchange for the performance, the booster club will receive three-quarters of the shop's gross receipts during that three-hour period. a. Let .f be the independent variable representing the gross receipts of the coffee shop

during the performance. Let 7 be the dependent variable representing the share of the gross receipts that the coffee shop will donate to the band boosters. Write an equation relating x and y.

b. Use the equation from part a to complete the following table. X, T O T A L G R O S S R E C E I P T S ($) 250 500 750 1000

y, B O O S T E R S ' S H A R E ($)

C. If the coifee shop presents you with a check for $650, what were the gross receipts during the performance? Estimate your answer using a numerical approach.

ACTIVITY 1.9 FUND-RAISER REVISITED 85

d. The graph of the equation determined in part a is given below. Use a graphical approach to estimate the gross receipts from part c.

200 400 600 800 1000 1200 Total Gross Receipts (in dollars)

3. A tennis ball is dropped from the top of the Empire State Building in New York City. The following table gives the ball's distance from ground level at a given time after it is dropped.

T I M E ( S E C ) 1 2 3 4 5 6 7

D I S T A N C E ( F T ) 1398 1350 1270 1158 1014 838 630

The Empire State Building is 1414 feet tall. Use the information in the table to approxi­mate the time when the ball will have fallen half the height of the building.

4. a. The depth (inches) of water that accumulates in the spring soil from melted snow can be determined by dividing the cumulative winter snowfall (inches) by 12. Trans­late this statement into an equation, using /for the accumulated inches of water and n for the inches of fallen snow.

b. Determine the amount of water that accumulates in the soil if 25 inches of snow falls.

86 CHAPTER 1 INTRODUCTION TO PROBLEM SOLVING AND MATHEMATICAL MODELS

c. Write an equation that can be used to determine the total amount of winter snow that accumulates 6 inches of water in the soil.

d. Solve the equation in part c using a numerical approach.

e. Solve the equation in part c using a graphing approach.