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Unformatted text preview: MATH 111 I Sample Exam 4 Exam is on Thursday, November 5 BRING YOUR ID TO THE EXAM BRING YOUR GRAPHING CALCULATOR TO THE EXAM
You may not use a TI—89. Ofﬁce Hours Wednesday November 4: 9 — 2 and 5:15 —6 The exam covers topics from Function Composition with Graphs and Tables to
Exponential Growth. (Exponential Decay is not on this test.) 1. Write 10—4 = .0001 as an equivalent equation involving logarithms.
(Use the deﬁnition of logarithm.) 2. Solve for as. log(3$ + 7) = 1 3. Evaluate log; 23 using the change of base formula and your calculator.
Write all the digits. 4. Use the Rule of 70 to answer these questions.
a. f (t) = 20(1.048)‘, with t in years. Find the doubling time.
b. Find the growth rate if doubling time is 14 weeks. 5. f(t) = 20(1.048)‘, with t in years.
Find the doubling time using 2nd CALC intersect.
Find the doubling time algebraically (show your work.) 6. Write the exponential equation that has an initial value of 570 and a growth
rate of 16%. 7. A : 16000(1.02)t What is the growth factor? growth rate? 8. Solve for ac. 6"” = 25
Give the exact answer and a decimal approximation. 9. Solve for :3. 2x+5 = 32m—4
Give the exact answer and a decimal approximation. 20m+3
173+5 10. f(zr:)= Find f‘1($). A = P (1 + g) (m) A = Pew 11. How much money will you have in an account after 10 years if you invest $6000
at 4.7% compounded continuously? Round to dollars and cents. 12. How much money should be invested at 5.8% compounded quarterly in order
to have $5000 after 10 years? Round to dollars and cents. 13. How much money will you have in an account after 15 years if you invest $8000
at 5.2% compounded monthly? Round to dollars and cents. 14. How much money should be invested at 6% compounded continuously in order
to have $10000 after 20 years? Round to dollars and cents. 15. How long will it take for $2000 to grow to $7000 if invested at 5.5% compounded
continuously? At 8% compounded quarterly? 16. Write the equations for these graphs. i
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 17. Solve for a: : 10g5 (x — 1) + log5 (x + 3) = 1.
18. Solve for :r : logz (a; + 5) — logz (x —— 2) = 3. . 19. Solve for a: : 2log2 (:13) — logz (1r — 1) = 2. 20. Find the intercepts of the following functions.
Give the exact answer and a decimal approximation.
Remember to write the intercepts as points!
a. y = e3+2 — 4
b. y=1n(a:+5)+1 21. Here are the graphs of y = ﬁx) and y = g(:r). Find (9 o f)(2). :1 23. Solve for 11;“. Just give the exact answer. 125 25 =
1 + 267‘” MM“ mﬁ SW?” Exam at M
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 Fall '08
 HITCHCOCK

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