Growth and Decay
Name:_________________________
Date: __________________ Per.____
PreAP Classwork
1. There are 4 parts to the exponential function. Label what each represents:
y  a bx
2. Identify which graph is growth or decay. The equations for each graph are given. Write an
inequality to describe what you notice about a and an inequality to describe what you notice about b.
Exponential ____________
y  100  (0.5)x
Exponential ____________
y  1  (2)x
when a ____ &
when a ____ & b______
b
_____
3. In 1995, there were 285 cell phone subscribers in the small town of Brushville. The number of
subscribers increased by 75% per year until 2005. How could we find the number of cell phone
subscribers in Brushville in 2004? (Don't consider a fractional part of a person.)
a) What is the initial number of subscribers? What variable does this represent?
b) For the variable b, we need to start with 100% (of those subscribers) and increase that by 75%.
How do we write 100% as a decimal? _____ How do we write 75% as a decimal? ______
So, how do we write b?
Growth: b  ________________________
c) Now the equation is
4. To find the number of subscribers in 2004, we need to determine the number of time intervals.
d) What is the number of time intervals? (years) ______
e) Find the number of subscribers in 2004. ___________
5. A black Mustang costs $40,000 new and depreciates at a rate of 12%.
a) What is the initial cost of the car?
b) What variable does this represent?
c) For the variable b, we need to start with 100% (of cost of car) and decrease by 12%.
How do we write 100% as a decimal? ______ How do we write 12% as a decimal? _______
So, how do we write b?
Decay: b  ________________________
d) Now the equation is
e) Find the value of the Mustang after 5 years.
f) How long will it take for the value of the mustang to be $18,000?
6. Label whether the equation below represents exponential growth or exponential decay:
A = a(1+ r )t
A = a(1- r )t
______________________________
___________________________________
7. Determine whether the following are equations of exponential growth or decay and determine
the % of growth or decay.
1
a) y  6(1.2)x
b) y  2(0.56)x
c) y  (0.5)x
3
d) y  0.75(1.7)x
e) y  1.2(4)x
f) y  4(1.02)x
8. Complete the box to the right:
Doubles:
b 2
______% increase
9. A population of 225 toy poodles doubles every year.
Triples:
b 3
______% increase
a) Write an equation that models this situation.
b) Find the population after 3 years.
c) Find the population 4 years ago.
Quadruples: ______% increase
b 4
If b  9 , what would the %
increase be?
If there is a 700% increase, what
is the value of b ?