CK12 Calculus - Single Variable

1995 55

2000 58

2005 60

a. Makea scatterplot of the data.
b. Basedon your sketch,shouldyou use a linearor quadraticmodelfor the data?
c. Find a modelfor the data.
d. Can you explainwhy the data seemsto dip at first and then grow?

5. Basedon the modelfor the previousproblem,whenwill womenmakeas muchas men?Is your answer
   a realisticprediction?


6. The averagepriceof a gallonof gas for selectedyearsfrom 1975–2008is givenin the followingtable:

Year Cost

1975 1

1976 1.75

1981 2

1985 2.57

1995 2.45

2005 2.75

2008 3.45

a. Makea scatterplot of the data.
b. Basedon your sketch,shouldyou use a linear, quadratic,or cubicmodelfor the data?
c. Find a modelfor the data.
d. If gas continuesto rise at this rate, predictthe priceof gas in the year 2012.

7. For the previousproblem,use a linearmodelto analyzethe situation.Doesthe linearmethodprovidea
   betterestimatefor the predictedcost for the year 2011? Why or why not?


8. Supposethat you place in a bankaccountwhereit growsexponentiallyat a rate of contin-
   uouslyover the courseof five years.The tablebelowshowsthe amountof moneyyou haveat the end of
   eachyear.

Year Amount

0 1000

1 1127.50

2 1271.24

3 1433.33

4 1616.07

5 1822.1 1

6 2054.43

a. Find the exponentialmodel.