Exponential and Logarithm Word Problems – Math 12
1. Strontium-90 has a half-life of 25 years. How many years does it take for a 20 mg sample
to decay to a mass of 2 mg?
(83.05 yrs)
2. Radium-221 has a half-life of 30 s. How long will it take for 95% of it to decompose?
(129.66 seconds)
3. If 25 mg of a radioactive element decays to 20 mg in 48 hrs, find the half-life of the
element.
(149.10 hrs)
4. A sample of Radon-211 decays to 30% of its original mass in 29 hours. What is the half-life
of Rn211?
(16.70 hrs)
5. Bob Brown invests $5000 in an account that pays 9% per annum compounded semiannually. How long must he wait (to the nearest half year) in order to have $8400 for the
purchase of a new car?
(6 yrs)
6. If, under certain conditions, the number of bacteria in a jug of milk doubles in one hour, in
how many hours will it be 100 times the original number?
(6.64 hrs)
7. A bacteria culture starts with 50 000 bacteria. After 60 minutes the count is 125 000.
a) What is the doubling period? (45.39 min)
b) b) When will there be one million? (196.17 min)
8. Bill invested a sum of money. The interest rate was 6% per annum, compounded
quarterly. After 10 years, Bill had approximately $4500. What was his initial investment?
(approximately $2480.68)
9. When rabbits were first introduced to Australia last century, they had no natural enemies
so their numbers increased rapidly. Assume that there were 60 000 in 1865, and that by
1867 the number had increased to 2 400 000. Assume exponential growth.
a) Write an equation for this function. ( R  60 000(40) 2 )
b) How many rabbits would you predict in 1870? (607 157 310.8)
t
10. Phoebe Small is out Sunday driving in her rocket ship. She fills up with fuel at the Scorpion
Gulch Rocket Fuel Station, and takes off. When she starts the last stage of her rocket, she
is going 4230 miles per hour. Ten second later she is going 6850 mph. While the last stage
is running, you may assume Phoebe’s speed increases exponentially with time.
a) Generate an equation to represent Phoebe’s rate “R” (in mph) in terms of time “t”
t
(in seconds). R  4230(1.6194) 10
b) In order to go into orbit, Phoebe must be going 17 500 mph. She took in enough
fuel for 30 seconds. Will she orbit? Explain. (17 963.99 in 30 sec. – fast enough)
c) What is the minimum length of time that last stage could run and still get Phoebe
into orbit? (29.4 seconds)
d) How long would the last stage have to run to get Phoebe going 25 000 mph so that
she could go off to the Moon? (36.88 seconds)