AFDA – Unit 5: Exponential and Logarithmic Functions
Day 2 Notes: Real World Exponential Functions
Name: _________________
Block: _____ Date:_______
Today we will learn…
 How exponents are used in the real world
Exponential Growth
Exponential Decay
𝑦 = 𝑎(1 + 𝑟)𝑡
𝑦 = 𝑎(1 − 𝑟)𝑡
𝑦 = ___________________________________________
𝑎 = __________________________________________
𝑟 = ____________________________________________
𝑡 = __________________________________________
What generalizations can you make about the base for:
 Exponential growth?
 Exponential decay?
Collector Car. The owner of a 1953 Hudson Hornet convertible sold the car at an
auction. The owner bought it in 1984 when it’s value was $11,000. The value of the car
increased at a rate of 6.9% per year since purchase.
𝑎=
𝑟=
𝑡=
 Exponential growth or decay? (sketch the curve)
 Write a function that models the value of the car over time.
 The auction took place in 2004. What was the approximate value of the car at the
time of the auction? Round your answer to the nearest dollar.
Compound Interest. Joe deposited $40 in a savings account earning 5% interest,
compounded annually.
𝑎=
𝑟=
𝑡=
 Exponential growth or decay? (sketch the curve)
 Write a function that models the amount in Joe’s account over time.
 To the nearest cent, how much will be in his account after 3 years? Round to the
nearest cent.
Rumors. A student decides to spread a rumor about you at the beginning of the school
day (9:00AM) and it spreads at a rate of 100% each hour.
𝑎=
𝑟=
𝑡=
 Exponential growth or decay? (sketch the curve)
 Write a function that models the number of people that know the rumor over time.
 If the school day ends at 4:00PM, how many people will know the rumor by the
end of the day? (This should make you think twice about spreading rumors!)
Online Shopping. A website that sells funny t-shirts has experienced a decrease in
customers at a rate of 5% per month.
𝑎=
𝑟=
𝑡=
 Exponential growth or decay? (sketch the curve)
 Write a function that models the number of customers that buy shirts if they had
43,000 customers this month.
 How many customers should the website expect to have two months from now?
Caffeine. Danielle just drank a cup of coffee to help her stay awake. The coffee had
150 milligrams (mg) of caffeine in it and her body processes 15% of the caffeine every
hour.
𝑎=
𝑟=
𝑡=
 Exponential growth or decay? (sketch the curve)
 Write a function that models the amount of caffeine in Danielle’s body over time.
 How much caffeine will be left in Danielle’s body after 3 hours? Round to two
decimals.
Radioactive Decay. A specific type of iron has a half-life of 45 days.
𝑎=
𝑟=
𝑡=
 Write a function that models the amount of iron that will remain over time if you
begin with 432 grams.
 How much iron will be left after 135 days?
Fable. There is a well-known fable that the ruler of India was so pleased with one of
his palace wise men, who had invented the game of chess, that he offered this wise
man a reward of his own choosing. The wise man, who was also a wise
mathematician, told his Master that he would like just one grain of rice on the first
square of the chess board, double that number of grains of rice on the second square,
and so on: double the number of grains of rice on each of the next 62 squares on the
chess board (there are 64 total squares on a chessboard). This seemed to the ruler to
be a modest request, so he called for his servants to bring the rice. How surprised he
was to find that the rice quickly covered the chessboard then filled the palace!
𝑎=
𝑟=
𝑡=
 Write a function to illustrate the situation and then complete the table below.
Square
Number
Grains of Rice on Each Square
Pattern
0
1
20
1
2
21
2
3
4
5
6
7
8
9
10
11
12
13
…
 How many grains of rice did the King have to place on the 64th square of the
board? (𝑡 = 63)