Exponential Context Problems
Teachers: Here you will find a bank of exponential context problems to choose from.
Students should use multiple representations (equations, tables, graphs) to examine these
problems. This is also an excellent opportunity to talk about the growth rate of an
exponential function. Some ideas: assign different groups one of the problems for a
presentation, allow students to choose 3 to solve, choose a few to use in group settings then a
few for independent practice, etc.
1. Ribbons: Carmen purchased one long piece of ribbon from the craft store that she was
going to cut into smaller pieces to tie onto gift bags. She started by cutting the ribbon into
three equal sized pieces as shown below. She then took each resulting piece and cut them
into 3 equal sized pieces. If she continued in this manner, write an equation that would give
the number of pieces of ribbon after the nth cut?
Number of Cuts
Pieces of Ribbon
0
1
2
2. Family Trees: A portion of Amal’s family tree is shown below. Write a function that would
be used to find the number of people in generation g?
Maternal
Grandmother
Mother
Maternal
Grandfather
Amal
Paternal
Grandmother
Father
Paternal
Grandfather
Generation 1
Generation 2
Generation 3
3. Rumors: At Highland High, Sydney, a 10th grader, decides to start a rumor that Salt Lake
District is going to declare March 17 a holiday and close school for the day. On the first day
of school, she tells 3 students the rumor and gives them instructions to repeat the rumor
(and instructions) to 3 more students the next day, etc. If each student follows these
instructions, how many students will hear the rumor on day 6? On day 10? On the nth day?
4. Radioactive Decay: Some carbon atoms are radioactive. The radioactive carbon atom,
carbon-14, has a half-life of about 5700 years. The half-life is the time it takes for one-half
the radioactive atoms to decay. How long it will take for the 50 grams of carbon-14 in a
dead tree to completely decay (close to zero grams left)?
5. Medicine: You are an Olympic athlete scheduled to compete on Friday at 4:00 PM. On
Thursday morning you awaken with a bad cold and consider taking a cold medication. You
know drug testing will take place immediately prior to the competition and the drug test is
capable of detecting 1 or more milligrams of medication in your system. After each 4-hour
time period your body will have dissipated one-fourth of the remaining drug. If you take a
16 milligram dosage at 8:00 AM, will you pass the drug test and be able to participate?
6. Cars: A car that is originally valued at 32,000 dollars loses 18% its value every 3 years.
What will be the value of the car after 12 years?
7. Salaries: You recently graduated from college and got a job with a starting salary of
$42,000. You are guaranteed a raise of 3% each year. What will your salary be after 5 years?
After 15 years? After n years?
8. Email Chains: Laura received the following email: “Forward this email to 50 people or the
most terrible bad luck will happen to you.” One man broke the chain and a flower pot fell on
his head, giving him a terrible headache which continues to this day. Assume that Laura has
many superstitious friends and the chain is not broken. Also, assume that it takes a day to
send the email along. How many people will have received the email after 5 days? After 10
days? After n days?
9. Compound Interest: You deposit $500 in a CD account that pays 4% annual interest
compounded yearly. What is the account balance after 5 years? After 30 years? After n
years?