Download Unit 2 Review Sheet NAME: DATE: _____________ Period

Unit 2 Review Sheet
Exp / Log Functions
NAME: _______________________________ DATE: _____________ Period : _________
Review Sheet
SCORE:
Graph exponential and logarithmic functions and identify domain, range, and transformations
Model situations with exponential formulas (word problems)
Evaluate / solve equations using appropriate properties / inverses
FUNCTIONS: ______ / _______ = _______%
FUNCTIONS
1. Write
43x = 64 in logarithmic form.
________________________________
2. Write
ex+2 = 5 in logarithmic form.
________________________________
3. Write log81 9 = ½
4. Write
in exponential form.
________________________________
ln 5 = y in exponential form.
________________________________
5. Evaluate (4 decimal places) log5 10
6. Condense
7. Expand
8.
9.
________________________________
8log3 x + 2 log 3 y
________________________________
log x9y7
w
________________________________
State whether f(x) = 2 (1.2)x shows exponential growth or decay.
________________________________
Graph
y = 3x + 1 + 4
and identify:
10. Graph
y = – log2 (x – 6)
and identify:
Domain: ___________
Domain: ___________
Range: _____________
Range: _____________
Transformations: ____________________________
Transformations: ______________________________
Round 4 decimal places for problems 11 – 16.
11. Solve
log ½ x = 5
12. Solve
(2)m + 7 = 16
13. Solve
log5 n = 2 log5 3 + ½ log5 100
14. Solve
ln (x + 1) = 3
15. Solve
ln 4x – 2 ln 6 = ln 75
16. Solve
e– 5x = 20
17. Given the table below answer the following questions:
Years
Population of Giraffes in the U.S.
(in thousands)
1900
1920
1950
1985
2005
2010
8
22
38
57
73
96
a.
Find the exponential regression equation for the data (round to 2 decimal places).
b.
Predict the population of giraffes living in the U.S. in 2025 (round to the nearest whole number).
18. There is a culture of bacteria that is reproducing at a rate of 8% each hour. If there were initially 1500 bacteria
in the culture find the following:
a. How many will there be after 7 hours (round to the nearest whole number)?
b. When will the culture reach 2500 bacteria (round to the nearest whole number)?
19. Sam deposited $2500 in a savings account that earns 5.75 % interest compounded continuously. How long will
it take him to double his money (round to two decimal places)?
20. A piece of machinery valued at $150,000 depreciates at a fixed rate of 9% per year. After how many years will
the value have depreciated to $100,000 (round one decimal place)?
Performance Task - FUNCTIONS
21. The Jones Corporation found that its annual profit could be modeled by the exponential equation y = 8(1.01)t,
while the Davis Company’s annual profit is modeled by y = 7(1.05)t. For both equations, profit is given in millions of
dollars, and t is the number of years since 2005.
a.
Find each company’s annual profit for 2015.
b. In which company would you prefer to own stock? Explain – Indicate how a comparison of the two
company’s would support your decision.
Mixed Review:
22. Solve y = 3x – 5
2x – 6y = 14
24. Write the quadratic function represented by the graph.
(do NOT round)?
23. Solve
4 │x – 2│+ 1 > 9
( -1, 0)
( 3, 0)
( 1, -4)