Material in questions 4 & 5 will be covered on Test 4 during Spring 2007.
Math 105 C Test 3 Carter Name________________________
Show all work in order to receive credit. 11/15/06
1. Sketch the graph of each function by hand.
i. f(x) = - (x+2)2 + 6. ii. y = log3(x) (12)
2. Algebraically find a formula for h(x). Show your steps. (10)
3. Simplify: (10)
i. log7 49 ii. log81 iii.
7
log 5
7
x
iv. log216
4. Solve. (15)
i. 2x+3 = 5 ii. log(x-1) = 2 iii. 3( 2x ) = 4x iv.
3
2log 6
3
5. Use the rules of logarithms to rewrite 2 log(4x) – log(8) as a single logarithm. (5)
6. Office Max’s web site lists the price of a TI-84 Plus graphing calculator as $119.99. Suppose
someone predicts that the cost of the calculator will go down by $4 each year.
i. Find a mathematical model for the price of the calculator. Define your variables.
ii. Use the model to predict the price of the calculator in 2010. (10)
7. In a laboratory experiment, E. coli doubles every half hour. There are initially 100 E. coli present.
i. How many are present in 1 hour? In 2 hours?
ii. Find a function for the number of E. coli present t hours after the start of the study.
iii. How many are present after 6 hours?
iv. When will 5,000,000 E. coli be present? (12)
8-9. Plot the data. Choose an appropriate model and describe why you chose that model
(concavity, asymptotes, slope, increasing/decreasing, etc.). When recording model, write the
coefficients to 4 decimal places. Then use the model to answer the question(s).
8. The average price in dollars per 1000 cubic feet of natural gas for residential use in a county for
selected years is given in the table. Find a model for the price as a function of years since 1980.
What does the model predict that the price for 1000 cubic feet of natural gas would be in 2002?
When does the model predict that the price first exceeded $6.00? (Round to the nearest year.)
(
1
2
)
9. The IQ scores, rounded to the nearest 10, for a group of people are summarized in the table.
Determine a model for the data. Estimate the IQ score of the maximum number of individuals
according to the model.
(12)
Year 1980 1982 1985 1990 1995 1998 2000
Price ($) 3.68 5.17 6.12 5.80 6.06 6.82 7.71
IQ Score
# of
People
70 53
80 76
90 90
100 91
110 73
120 52
130 18
x h(x)
0 5
1 15
2 45
3 135
4 405