Name: __________________________________
1. For y = 3 x , complete the following:
Algebra 2 Unit 5 Exam Review
Describe the translation. Give the asymptote.
Label as growth or decay.
a) exponential growth or decay? b) y-int_____________
2. f(x) = 2(0.75) x+1 – 4 c) asy ______________ d) Graph!
11
10
9
8
7
6
5
4 y
3. y = -4(1.3) x + 1
3
2
1
–6
–7
4. An antique ring bought for $500 increases
–10
–11 x –11 –10 –9 –8 –7 –6 –5 –4 –3 –2 –1
–1
1 2 3 4 5 6 7 8 9 10 11
–2
Write an exponential function to model each situation. Then, find the value of the function after three years, to the nearest dollar.
–4
–5
5. A $22,500 car depreciates 11% each year.
6. You invest $1000 in an account. Find the value of each of the accounts after 4 years.
Which account gives you the best deal? a. 4.2% interest compounded continuously
7. Carl plans to invest $800 at 7.25% interest, compounded quarterly. How much money will he have gained in interest in 10 years? b. 4.2% interest compounded monthly c. 4.2% interest compounded weekly
8. Barium-122 has a half-life of 2 minutes. A fresh sample weighing 80 g was obtained. If it takes 10 minutes to set up an experiment using barium-122, how much barium-122 will be left when the experiment begins?

Write each equation in logarithmic form. Evaluate.
9.
4
2 =
16
11. log
2
32
12. log
0.5
16
10.
2
-
2 =
0.25
13. log
3
ç
æ
è
1
27
ö
ø
÷
Write each logarithmic expression as a single logarithm. Simplify if possible.
15. log 5
+ log 2
16.
4 ln x
+ ln 7
14. log
6
1,296
Expand the logarithm.
17. log 3 xy
4 18. log 𝑟𝑠 𝑡 2
Solve each logarithmic or exponential equation. Round to the nearest hundredth if necessary.
19. log
3
(10-4x)=log
3
(10-3x) 20. log
2
(x 2 + 35) = log
2
(-12x -1)
21. logx + log7 = log37 22. log
3
(x 2 -4x) = log
3
(16 + 2x)
23. logx = -2 24. ln(3x + 2) – ln2 = 1
25. 2log
4
(2r)=2 26. e
3 x +
2
=
10

27. Suppose $1500 is deposited in a savings account. If the interest rate is 3.5% compounded continuously, after how many years will the amount in the account be doubled?
Identify the sequence as arithmetic, geometric or neither. If arithmetic or geometric, state the common difference/common ratio and list the next 3 terms.
28. 3, -8, -19, … 29. 3, -9, 27, … 30. 2, 3, 5, …
Find the 1 st , 5 th and 12 th term of the sequence.
31. a n
= 3 + 4(n – 1) 32. A(n) = 3(-2) n-1
33. A ball dropped from a height of 30 m rebounds 80% of the distance fallen. a. Is this arithmetic or geometric? b. What is d or r? c. What is the first term? d. Write an equation. e. How high does the ball rebound after the 3rd time it hits the ground?

34. In his first hay-baling trip around a field, a farmer makes 123 bales. In his second trip he makes 11 fewer bales. Because each trip is shorter than the preceding trip, the farmer estimates that the same pattern will continue. a. Is this arithmetic or geometric? b. What is d or r? c. What is the first term? d. Write an equation. e. Estimate the total number of bales made if he makes 6 trips around the field.
Describe each sequence as arithmetic, geometric or neither. Find the appropriate common difference or common ratio. Then, find the 10 th term of the sequence. FRACTION!
35.
-8, -22, -36, … 36.
3, 12, 48, 192, …
Arithmetic? Geometric? Neither? d = ______ or r = _________
A(10) = _________
Arithmetic? Geometric? Neither? d = ______ or r = _________
A(10) = _____________
Write out the terms of the series. Find the sum.
37.
n

5  n

1
( 8 n

15 )
Sum ____________ n

8
38.
 n

4
1
2
( 4 ) n

1
Sum _____________
39. A grandfather invests $1000 into an account that with a 4.2% interest rate compounded monthly when his granddaughter is born. The account is now worth $2852.42. To the nearest year, how old is the granddaughter? (keep 4 decimal places)