Math-180-Practice Exam #2
Name___________________________________
Date: _____________________
Instructions: Show all work neatly. Answers without support will receive no credit. Your answers will be evaluated on
the correctness, completeness and use of mathematical concepts we have covered. Box your final answer and write your
answers in the answer column when possible.
Graph the function by making a table of coordinates.
1 x
1) f(x) =
5
1)
Graph the function.
2) Use the graph of f(x) = 2x to obtain the graph of g(x) = 2 x - 1.
Solve the problem.
3) The population in a particular country is growing at the rate of 1.4% per year. If 3,819,000
people lived there in 1999, how many will there be in the year 2007? Use f(x) = y0 e0.014t
and round to the nearest ten-thousand.
Use the compound interest formulas A = P 1 +
2)
3)
r nt
and A = Pe rt to solve.
n
4) Find the accumulated value of an investment of $17,000 at 6% compounded annually for
13 years.
1
4)
Write the equation in its equivalent logarithmic form.
5) 6 3 = 216
5)
Write the equation in its equivalent exponential form.
6) log 125 = 3
5
6)
Evaluate the expression without using a calculator.
1
7) log6
6
7)
Graph the function.
8) Use the graph of log x to obtain the graph of f(x) = log (x - 1).
5
5
8)
Find the domain of the logarithmic function.
9) f(x) = log (x + 1)
6
9)
Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
xy4
10) logb
10)
z6
Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose
coefficient is 1. Where possible, evaluate logarithmic expressions.
1
11) 8 ln x - ln y
11)
4
12) 4 log4 2 +
1
1
log4 (r - 7) - log4 r
7
2
12)
Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places
13) log 20
7
13)
Solve the equation by expressing each side as a power of the same base and then equating exponents.
14) 2 (3x - 5) = 16
14)
2
Solve the exponential equation. Express the solution set in terms of natural logarithms.
15) 4 x + 7 = 5
15)
Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic
expressions. Give the exact answer.
16) log x = 5
16)
2
17) log x + log (x - 3) = 2
2
2
17)
18) log (3 + x) - log (x - 5) = log 5
18)
Find the inverse of the one-to-one function.
3
19) f(x) =
2x + 1
19)
Solve the problem.
20) Find out how long it takes a $3300 investment to double if it is invested at 9% compounded
r nt
quarterly. Round to the nearest tenth of a year. Use the formula A = P 1 +
.
n
3
20)