1. 7-1 Exponential Functions
Today’s Objective:
I can model exponential growth and decay.

2. Exponential Function 𝑦= 2 𝑥 𝑦=𝑎⋅ 𝑏 𝑥 𝑎≠0 y-intercept: (0, a) 0.0625-4 -2 -1 1 2 3
𝑎≠0
y-intercept: (0, a)
0.0625
a = starting value
0.25
b = Constant Multiplier
0.5
𝑏>1
Growth 1
0<𝑏<1
Decay 2 4
Domain:
All real #s 8
Range:
𝑦>0
Graph on calculator and sketch
x-axis is an asymptote.
a line a graph approaches
𝑦= 𝑥
𝑦= 4⋅2 𝑥
𝑦= 4 𝑥

3. Exponential Growth and Decay
𝑦=𝑎⋅ 𝑏 𝑥
You invest $1,000 in an account for 6 years at 5% annual interest.
What is your balance?
Amount after t time periods
Initial Amount
# of time periods
𝐴(𝑡)= ⋅ ( )
1000
0.05 6
𝐴(𝑡)=𝑎⋅ (1+𝑟) 𝑡
=1000 (1.05) 6
Growth factor:
r = % growth or decay written as a decimal
Growth: 𝑟> Decay: 𝑟<0 =$

4. Exponential Growth and Decay
𝐴(𝑡)=𝑎⋅ (1+𝑟) 𝑡
You invest $500 in an account for 5 years at 3.5% annual interest.
What is your balance?
Jackson High school had 2,100 students at the start of the school year and it is predicted to decrease by 1.5% each year. How many students will be at Jackson at the start of the 2020 school year?
𝐴(𝑡)= ⋅ ( ) 5
500
0.035
=500 (1.035) 5
=$593.84
When will the account be worth $1,000?
Use calculator table.
𝐴(𝑡)= ⋅ ( )
−0.015 5
2100
About
21 years
=2100 (0.985) 5
=1,947
𝑦 1 =500 (1.035) 𝑥

5. Endangered Species 7-1 p.439: 10, 14, 18-31
If the trend continues and the population of the Iberian Lynx is decreasing exponentially, how many Iberian Lynx will there be in 2014?
𝑦=𝑎⋅ 𝑏 𝑥 𝑎=
150 𝑏=
=0.8
𝑝(𝑡)=150⋅ (0.8) 𝑡
7-1 p.439: 10, 14, 18-31
𝑝(11)=150⋅ (0.8) 11
=12