Chapter 6 Review
1) Find the multiplier for each rate of exponential growth or decay. (Section 6.1)
a) 1% growth b) 7% decay c) 5.26% growth d) 0.4% decay
1.01 0.93 1.0526 0.996
2) Evaluate each expression. (Section 6.1)
a) 2x for x = 0.5 b) 10 (2)x for x = 0.6 c) 7 (0.5)x for x = -2
1.414 15.157 28
3) The initial population of bacteria in a lab test is 400. The number of bacteria doubles every 30 minutes. Predict the bacterial population at the end of (Section 6.1)
a) 2 hours b) 3 hours
400 ∙ 24 = 6400 400 ∙ 26 = 25600
4) Tell whether each function represents exponential growth or decay. (Section 6.2)
a) f(x) = 5.9 (2.6)x b) f(x) = 13 (0.7)x c) f(x) = 22 (0.15)x
growth decay decay
5) Find the final amount for each investment. (Section 6.2)
a) $1300 earning 5% interest compounded annually for 10 years.
A=13001+0.0511∙10=$2117.56
b) $720 earning 6.2% interest compounded semiannually for 5 years
A=7201+0.06222∙5=$977.06
c) $300 earning 4.5% interest compounded quarterly for 3 years
A=3001+0.04544∙3=$343.10
d) $2000 earning 3.5% interest compounded daily for 5 years
A=20001+0.035365365∙5=$2382.47
e) $3500 earning 1.2% interest compounded monthly for 10 years
A=35001+0.0121212∙10=$3946.00
6) Write each equation in logarithmic form. (Section 6.3)
a) 192 = 361 b) 203 = 8000 c) 11-3 = 11331
log19 361 = 2 log20 8000 = 3 log11 11331 = -3
7) Write each equation in exponential form. (Section 6.3)
a) log12 144 = 2 b) log3600 60 = 12 c) log11 114641 = -4
122 = 144 36001/2 = 60 11-4 = 114641
8) Solve each equation. (Section 6.3)
a) log2 x = 8 b) log7 x = -3 c) log2 8 = x
28 = x à x = 256 7-3 = x à x = 0.0029 2x = 8 à x = 3
d) 10x = 25 e) logx 16 = 2 f) 10x = 150
log10 25 = x à x = 1.398 x2 = 16 à x = 4 log10 150 = x à x = 2.176
g) log3 x = 5 h) log4 64 = x i) logx 81 = 4
35 = x à x = 243 4x = 64 à x = 3 x4 = 81 à x = 3