Download Exponential Word Problems

Exponential Word Problems
1. A certain strain of yeast cell doubles under certain conditions every 20 minutes. If there
were 350 initially, how many will there be in three hours?
2. A certain bacterial strain divides every hour producing two bacteria from every existing
one. If there were 200 bacteria in a culture, how many will there be after
a) 4 hours?
b) 8 hour?
c) n hours?
3. For a biology experiment, the number of cells present is 1000. After 4 hours the count is
estimated to be 256 000. What is the doubling period of the cells?
4. Calculate the amount A(t) for each investment for the time shown.
a) $500 invested at 12% compounded yearly for six years
b) $1000 invested at 13.5% compounded yearly for four years
c) $800 invested at 12.75% compounded yearly for seven years
5. Pascal joined an investment club and was guaranteed 11.5% compounded annually. The
minimum period of time was five years.
a) Calculate the amount of money received at the end of 5 years if $1500 was
invested in the club?
b) How much interest did Pascal actually receive for investing the money?
6. Health officials found traces in radium-F beneath the local library. After 70 days they
observed that a certain amount of the substance decayed to 14 of its original mass.
Determine the half-life of radium-F.
7. Radium is used in the making of luminous paint for watch dials. Raphael lost her watch
in a construction site. If it were found 8100 years later, what fraction of the original
luminosity would be left in the watch dial if the half life of radium is 1620 years?
8. How long will it take for a 1 gram sample of polonium-210 to lose all but
1
128
th of its
radioactivity if its half life is 140 days?
9. During the transportation of the isotope thorium-243 to a nuclear waste facility, a spill
occurred near a populated area. The area was evacuated and no one was to return
home until the above isotope decayed to 14 of its original radioactivity. If the half life of
thorium-243 is 24 days, how long was the area evacuated?
Application: Carbon Dating
How can scientists pinpoint the age of bones of animals that die so long ago?
Carbon-14 is a radioactive substance with a half life of 5760 yeas. It can be used to determine
how long ago a plant or animal lived. For example, suppose an animal while living absorbed
Carbon-14. It is subsequently buried by volcanic ash, and the animal can no longer assimilate
C14. The C14 is radioactive. In 5760 years, half the original C14 absorbed by the animal will be
left. If the scientist knows
 how much carbon -14 is left, M(t), and
 how much carbon -14 there was to start with, M
then the scientist can use the exponential equation
M (t )  M o 2
t
5760
or
M (t )  M o  12 5760
t
Half life: 5760 years
to calculate the number of years ago, t, the animal died. This method of determining the age of
living things is called carbon dating.
10. A bone found at an archaeological site was determined to be 19 000 years old. If the
amount of C14 in the bone was 0.47 grams, calculate the original amount of C14 in the bone.
11. In a recent dig, a human skeleton was unearthed. It was later found that the amount of
Carbon-14 in it had decayed to 1/16 of its original amount. If Carbon-14 has a half life of
5760 years, how old was the skeleton?