NAME
DATE
PERIOD
3-4 Word Problem Practice
Exponential and Logarithmic Equations
1. RADIOACTIVE DECAY The amount of radium A
present in a sample after t years can be modeled by
A = 𝐴0𝑒−0.00043𝑡,where 𝐴0 is the initial amount.
How long will it take 50 grams to decay to10 grams?
5. RADIOACTIVITY The amount of radioactivity in a
sample is given by the equation ln (N) –ln (𝑁0 ) = −kt,
where N is the current level, 𝑁0 is the originallevel, k is
the decay rate, and t is the time elapsed in hours. If the
decay rate is 0.070, how many grams would be left
after 24 hours if the original amount was 1000 grams?
2. INTERNET The table shows the number of hits an
Internet blog received for three weeks.
Week
Number
of Hits
1
1000
2
1250
3
1563
6. BIOLOGY A certain strain of bacteria in a perfect
growth medium doubles in population every 8 hours.
a. If there were 100 bacteria at t = 0hours, complete
the table below.
Time (hr)
8
16
24
32
64
Number of
doubles
a. Write an exponential model to find the number of
hits N in week w.
Population
b. In what week will the blog get10,000 hits?
b. Write an equation to model the number of bacteria N
at time t given𝑁0, the initial number of bacteria.
3. RICHTER SCALE The function used to measure the
magnitude R of an earthquake is given by R = 0.67 log
(0.37E) + 1.46, where E is the energy in kilowatt hours
that is released by the earth quake. If the magnitude of
an earthquake is 6.0,find the approximate energy
released.
c. Suppose a chemical is added that kills exactly one
half of the bacteria at the 16-hour mark. Write an
equation to find the number of bacteria after the
16-hour mark.
4. INTEREST RATE The effective annual yield E for
an account that is compounded n times per year at r
𝑟 𝑛
percent is given by the formula E = [1 + ] – 1.
𝑛
d. Using the formula in part c, find how long it will
take for the number of bacteria to reach 5000.
Suppose an account pays 5%. Use a calculator to find
how many compounding periods it would take for the
effective yield to be 5.1%.
Chapter 3
23
Glencoe Precalculus