Name__________________________________
Chapter 8 Review
Determine whether each function represents exponential growth or decay. State the
equation for the asymptote line. Then graph.
1) Y = ½(4)x + 1
2) f(x) = 2(0.5)x - 2
3) y = 2x-1
4) The price of a new home is $126,000. The value of the home appreciates 2% each year.
How much will the home be worth in 10 years?
5) A motorcycle purchased for $9000 today will be worth 6% less each year. For what can you
expect to sell the motorcycle at the end of 5 years?
6) How much did you initially invest if your balance is $3,500 after earning 6% interest
compounded quarterly for 5 years?
7) You invest $3200 into an account that compounds the interest continuously. What will you
have in your account at the end of 5 years if the interest rate is 4.5%?
8) I-123 is used in thyroid scans. It has a half-life of 13.2 hours. Write the exponential decay
function for a 45-mg sample. Find the amount remaining after 5 hours. Round to the nearest
hundredth.
Write each equation in exponential form:
9) log7 1 = 0
10) log17 289 = 2
11) log 10 = 1
12) ln 1 = 0
Write each equation in logarithmic form:
13) 252 = 625
14) 45 = 1024
1
15) 4-3 = 64
16) e-2 =
1
𝑒2
Evaluate each logarithm:
17) log3 27
18) ln 1
19) log5 (-125)
21) log26 26
22) log2 8
1
23)
log3 34x
20) ln e3x
24) ln (-2)
Write each logarithmic expression as a single logarithm (condense):
25) log6 25 – log6 5
26) 5 log x + 3 log x2
27) log3 2x – 5 log3 y
28) ln 16 – ln 8
29) 3 ln 3 + ln 9
30) 4 ln x + 3 ln y
Expand each logarithm:
30) log2
𝑥
𝑦𝑧
31) log
2𝑥 2 𝑦
3𝑘 3
32) ln 5𝑥 2 √𝑦
Solve: (round to the nearest thousandth when necessary)
37) ln (3x + 4) = 5
38) log4 (x + 4) = 1
39) 24x = 8
40) log 3x – log 5 = 1
41) 2 log x – log 3 = 1
42) log x – log 4 = -2
43) 10n-2 = 0.3
44) 4x – 5 = 12
45) ex-4 = 2
𝑡
46) The battery power available to run a satellite is given by the formula 𝑃 = 50𝑒 −250 , where P
is power in watts and t is time in days. How long can the satellite run if it requires 15 watts?
47) An initial investment of $100 is now valued at $149.18. The interest rate is 8%,
compounded continuously. How long has the money been invested?
48) A parent raises a child’s allowance by 20% each year. If the allowance is $8 now, when will
it reach $20.