Name ______Algebra II
Practice Test Unit 6
1) Write an equivalent expression using the properties of logs:
2) If log 6 = x and log 7 = y, then log 42,000 is equal to
(1) 1000xy (3) x + y + 3
(2) x + y + 2 (4) 3xy
3) Algebraically solve the system of equations below.
and
4) Bacteria being grown for research programs at a university grow at a rate of 75% every hour. If there are 45 bacteria in the population, how long will it take for the bacteria to reach 1000? Round to the nearest hundredth of an hour.
5) If a population decreases by 18.2% every 20 years, what was the percent decrease for every 5 years to the nearest tenth of a percent?
6) Which of the following is equivalent to
(1) (3)
(2) (4)
7) Consider the equation .
a) Determine the graph’s x-intercept algebraically.
Justify your answer.
b) State the equation of any asymptote(s).
c) Sketch the graph of the equation and be sure to
indicate the x-intercept.
d) State the domain. e) State the range.
f) Is the equation one-to-one? Explain.
g) Find f-1(x).
h) Given the equation g(x) = log4(x – 5) + 3, describe the transformation that occurred to
map f(x) onto g(x).
8) Express in simplest form:
9) If f(x) = 5x – 2 and g(x) = , find the value of .
10) Brent invested $5300 into an account that pays an annual interest rate of 4.3% compounded weekly. How much, to the nearest hundred dollars, will his investment be worth in 7 years?
11) Algebraically determine the y-intercept .
12) Write an exponential equation that passes through the following pairs of points:
and (3,32)
Solve each of the equations below.
13) 14)
15) 16) log216(x) =
Solve for x to the nearest ten-thousandth.
17) 18)
19) Jo-Jo puts $1500 into a savings account at an annual interest rate of 5% compounded continuously. To the nearest year, how many years will it take for the initial amount to quadruple in value?
20) Given the function, , find the average rate of change over the interval [3, 6].
21) The accompanying graph is a sketch of the function y = f(x) over the interval . Find the value of .