Exam 3 Review - Kent



Exam 3 Review

Sections 2.3, 3.1 – 3.5

Important Topics to know:

|Sec 2.3 - |Piecewise Functions: evaluate, graph |

| |p. 189 # 9, 10, 12, 23, 24, 25, 26, 49; also handbook p. 130 |

|Sec 3.1 - |Exponential functions: graphs, growth vs. decay, the number e, problem solving |

| |pp. 288 #2, 23, 25, 28, 31, 35 also Handbook: p. 141 |

|Sec 3.2 - |Logarithmic functions: log vs. exponential form, evaluating logarithms, natural log, common log, graphs, problem solving|

| |pp. 300 # 1-8, 15, 21, 22, 24, 27, 30, 35, 39, 40, 42, 51; also handbook, pp. 144-146 |

|Sec 3.3 - |Solving exponential and log equations: Properties of logs |

| |pp.314 # 1 – 10, 11, 12, 47, 54, 55, 57, 70. Also handbook: pp. 155 – 158, 166 |

|Sec 3.4 - |Exponential and log models: determining of data is exponential, writing models |

| |pp. 328 #1, 2, 5, 6, 13, 14, 15, 17, 23; also handbook, p. 134, 142, and extra worksheet |

|Sec 3.5 - |Investments and interest compounded annually, monthly, etc., continuous compounding, solving for the variable t in |

| |context. |

| |pp. 339 # 1, 2, 4, 15, 18, 19, 23, 28, 29, 33; also in handbook, p. 170 |

Things to know:

• A piecewise function is just a function with multiple parts defined by different rules (or formulas).

• Definition of a logarithm states if [pic], then [pic]

• List the Properties of Logarithms:

• When solving exponential equations, divide both sides by the initial value, then take the log (or ln) of both sides. Use the properties of logarithms to bring the variable down; then solve.

• When solving logarithmic equations, we eliminate the “log” in one of two ways. If you have log_____ = log ______ then set the arguments equal to each other and solve algebraically. If you have log _____ = k then put the equation in exponential form to solve.

• Identify a exponential function by looking a table of values

Try some of these:

1. Given the following exponential functions, determine if they show growth or decay.

A. y = 100(.80) n C. y = 2 -3x

B. y = .5(6 k) D. y = 5x

2. Write as a sum or difference of logs:

log[pic]

3. A bank compounds interest annually at 4.5%. How much money will you have in 9 years if you’re your

initial investment is $5000? (5)

Circle one:

A. $141,671.35 B. $7496.51 C. $5225.00

D. $7479.58 E. $7430.48 F. Other:

4. The graduated tax function where the tax is 6.5% on the first $25,000 of income, then

8% on any income over $25,000 is given in the following piecewise function:

g(i) = [pic]

Determine the tax payable on an income of $43,000.

5. Suppose Adamsville has an initial population of 3900 people and gains townspeople at a 3% rate each

year. The function of the population of the town is given as [pic], where t is the number of

years after its initial population.

Find how many years it would take for Adamsville to reach a population of 10,000 people.

Determine how many people live in the town after 12 years.

Sketch the graph of the function.

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