Download Math 109 Final Review

Math 109
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Sketch the graph of f HxL = 3 - 2-x-1
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Final Review
Find the exponential function f HxL graphed below.
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16. $3000 is invested into an account paying 4% annual interest compounded bimonthly. How long will it
take for the account to reach $3500?
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Simplify the following.
HbL
log3 81
5log5 3
5. Use a change of base in order to find the decimal approximation for log7 H10L . Give the result correct to
four decimal places.
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Find the domain of the following logarithmic function. gHxL = log5 H4 - x2 L
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Use the following graph of the logarithmic function f(x) to answer parts a and b.
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HaL
HbL
Find b where f HxL = logb x.
Find f -1 HxL.
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Solve the equation. 4 H1 + 75 x L = 9.
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Solve the equation log x+2 4 = 2.
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Solve the equation log6 x + log6 Hx + 1L = 1.
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‰ x x2 + 2 x ‰ x + ‰ x = 0
log4 H2 xL + log4 Hx - 2L = log4 Hx + 3L
15. $3000 is invested at an annual percentage rate of 8.5%. How long will it take the account to reach $5000
if the interest is compounded monthly? Use algebraic methods to solve.
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HaL
HcL
14. The half-life of Strontium-90 is 28 years. How long will it take a 50mg sample to decay to a mass of
32mg?
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log2 Hx + 5L = 3
Solve for x. Use algebraic methods.
HbL
Sketch the graph of the function f HxL = -3-x+2 + 1. Justify your answer.
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HaL
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Rewrite the expression in a form with no logarithms of products, quotients, or powers. lnI ÅÅÅÅÅÅÅÅ
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x2 +x-2
Solve the equation. log3 Hx - 1L - log3 x + log3 2 = 1
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Solve the equation graphically. x3 = ex+1 - 3
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HaL
The initial count in a bacteria culture was 241. After 5 hours, the count was 1000.
HbL
Assume the growth is exponential. Find a formula for the number of bacteria nHtL after t hours.
Predict the number of bacteria after 8 hours.