Chapter 8 Review
1) A bacteria culture starts with 3000 bacteria and doubles every hour. How much bacteria is present after 2.5 hours?
2) A bacteria culture triples every 4 hours and starts with 10,000 bacteria. Find the number of bacteria in the culture after 30 hours.
3) Strontium-90 has a half-life of 25 years. If there was 40 mg present initially, how much is left after 37 years?
4) Cm242 has a half-life of 163 days. If 10 grams are present initially, how much remains after one week?
5) The population of the state of Texas in 1950 was 7,711,194 people and grew from 1950 to 1980 at an annual rate of approximately 2%.
a) What is the growth factor?
b) Write a model to represent the situation.
c) What was the population in 1960 (Round to the nearest person)?
d) When will Texas reach a population of 20,000,000?
6) If the population of Anchorage, Alaska in 1970 was 28,900 and is decreasing at a rate of 2.6% per year.
a) What is the decay factor?
b) Write a model to represent the situation.
c) Estimate the population in 1995? Round to the nearest person.
d) When will Anchorage reach a population of 15,000?
7) Molly is the trust officer for an estate. She invests $15,000 into an account that carries an interest rate of 8% for 14 years.
a) What is the amount in the account if the interest is compounded monthly?
b) What is the amount in the account if the interest is compounded quarterly?
c) What is the amount in the account if the interest is compounded continuously?
8) Graph, identify the asymptote, and find the domain and range.
a) b) y = 27(3)x – 1 + 9c) y = log6 xd) y = log6 (x – 1) + 3
9) Write an exponential model given the following information.
a) (1, 1) (2, 3)b) (-3, 4) (-1, 1)
10) Evaluate each expression without a calculator. Show your work!
a) log4b) log366c) log327 – log31d) ½ log416 + log464
11) Write each expression as a single logarithm.
a) ln z – 3 ln xb) 4 log x + 3 log y
12) Expand each logarithm.
a) log7b) ln
13) Solve each equation. Round answers to the nearest hundredth.
a) 102n – 5 = 500b) 5x + 1 = 3c) 33n = 50
d) 11x – 50 = 12e) log 3x = 2 f) 4 log x = 4
g) log (3x – 2) = 3h) log 8 + log 2x = - 1 i) log x + log(x +3) = 1
j) 2log 3x – log 9 = 1k) 4ex = 10l) ex + 2 = 50
m) 4e3x – 1 = 5n) o) 6 – e12x = 5.2
p) eln5x = 20q) 4lnx = - 2 r) 2ln(3x – 4) = 7
s) – 7 + ln2x = 4t) 3ln e2x = 12u)
v) 3 – 4ln(8x + 1) = 12