Algebra 1
Name:___________________________
Unit 5 – Day 1 – Notes
Unit 5 – LT 1 & 2
Date:__________Period:______
Learning Target 1: I can determine if an exponential function is a growth/decay using a table or graph.
Learning Target 2: I can identify key features from graphs and tables.(y-intercept and asymptotes)
EQUATIONS OF EXPONENTIAL FUNCTIONS:
The equation of an exponential function has an _________________ that includes a ____________________.
The general form of an exponential equation is…
𝒚 = 𝒂 ∙ 𝒃𝒙
b = the exponential base
Growth
Decay
Graph the following exponential functions in your graphing calculator. Determine which graphs are exponential
growth and which graphs are exponential decay. Then use it to create a rule based on the equation to determine
when a function is exponential growth or decay.
a. 𝑦 = 2 ⋅ 3𝑥
b. a. 𝑦 = −4 ⋅ 0.2𝑥
c. 𝑦 = 0.5𝑥
Growth or Decay
Growth or Decay
Growth or Decay
d. 𝑦 = 2𝑥
e. a. 𝑦 = 2 ⋅ 0.9𝑥
f. 𝑦 = ⋅ 4𝑥
Growth or Decay
Growth or Decay
Growth or Decay
2
3
1. Determine the exponential base of the following exponential equations as well as if they are GROWTH or DECAY.
1𝑥
a. 𝑦 = 4 ⋅ 7𝑥
b. a. 𝑦 = −4 ⋅ 3𝑥
c. 𝑦 = 3
b = __________
b = __________
b = __________
Growth or Decay
Growth or Decay
Growth or Decay
d. 𝑦 = 2
e. a. 𝑦 = 2 ⋅ 0.25𝑥
f. 𝑦 = 3 ⋅ 2.1𝑥
b = __________
b = __________
b = __________
Growth or Decay
Growth or Decay
Growth or Decay
3𝑥
2
TABLES OF EXPONENTIAL FUNCTIONS:
As the x values increase, the y-values _________________ for an exponential GROWTH function.
As the x values increase, the y-values _________________ for an exponential DECAY function.
The exponential base can be found from an exponential function’s table by determining the factor that the y – values
are being multiplied by. (Hint: for difficult tables, divide a y-value by its previous y-value.
2. Determine if the following tables represent exponential growth or decay. Then calculate the exponential base.
a.
b.
c.
b = __________
b = __________
b = __________
Growth or Decay
Growth or Decay
Growth or Decay
d.
e.
f.
b = __________
b = __________
b = __________
Growth or Decay
Growth or Decay
Growth or Decay
SITUATIONS OF EXPONENTIAL FUNCTIONS:
Examples of Exponential Growth:
Examples of Exponential Decay:
3. Are the examples of exponential function situations below, GROWTH or DECAY?
a. Every month, Allison spends half of the money she has in her savings account.
b. Every week that Janet does all of her chores her allowance will increase by 10%.
c. Jesse bought two rabbits. Every month the rabbits reproduce and double the amount of rabbits she has.
d. Jacobs currently has 2259 students this year. The student population is growing 5% each year.
e. You purchase a car, but the value of the car depreciates by 10% each year.
GRAPHS OF EXPONENTIAL FUNCTIONS:
Review: The DOMAIN of a function is all the possible x-values.
The RANGE of a function is all the possible y-values.
4. Find the Domain and Range of each. Write each in interval notation.
a.
b.
c.
Domain:____________________
Range:____________________
Domain:____________________
Range:____________________
Domain:___________________
Range:____________________
The END BEHAVIOR of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or
negative infinity. Find the end behavior of the graphs above.
as 𝑥 → −∞, 𝑓(𝑥) →_________
as 𝑥 → −∞, 𝑓(𝑥) →_________
as 𝑥 → −∞, 𝑓(𝑥) →_________
as 𝑥 → +∞, 𝑓(𝑥) →_________
as 𝑥 → +∞, 𝑓(𝑥) →_________
as 𝑥 → +∞, 𝑓(𝑥) →_________
The HORIZONTAL ASYMPTOTE is a horizontal line that the graph of a function approaches but never reaches.
Find the equation of the horizontal asymptote of the graphs above.
____________________
____________________
5. Find the key information from the graphs of the exponential functions.
Growth or Decay:___________
Domain:___________________
Range:____________________
as 𝑥 → −∞, 𝑓(𝑥) → ____________
as 𝑥 → +∞, 𝑓(𝑥) → ____________
Horizontal Asymptote_________
Y-intercept: ______________
____________________
Growth or Decay:___________
Domain:___________________
Range:____________________
as 𝑥 → −∞, 𝑓(𝑥) → ____________
as 𝑥 → +∞, 𝑓(𝑥) → ____________
Horizontal Asymptote_________
Y-intercept: ______________
Growth or Decay:___________
Domain:___________________
Range:____________________
as 𝑥 → −∞, 𝑓(𝑥) → ____________
as 𝑥 → +∞, 𝑓(𝑥) → ____________
Horizontal Asymptote_________
Y-intercept: ______________
Growth or Decay:___________
Domain:___________________
Range:____________________
as 𝑥 → −∞, 𝑓(𝑥) → ____________
as 𝑥 → +∞, 𝑓(𝑥) → ____________
Horizontal Asymptote_________
Y-intercept: ______________
Algebra 1
Name:___________________________
Unit 5 – Day 1 – Homework
Unit 5 – LT 1 & 2
Date:__________Period:______
Learning Target 1: I can determine if an exponential function is a growth/decay using a table or graph.
Learning Target 2: I can identify key features from graphs and tables.(y-intercept and asymptotes)
Are the following tables, equations and situations growth or decay? Find the exponential base.
X
0
1
2
3
1.
Y
1
2
4
8
X
2
3
4
5
Growth or Decay
2.
b = _____________
X
0
1
2
3
4.
Y
10,000
8,900
7,921
7,049.69
Growth or Decay
𝑦 = 2 ∙ 3𝑥
Growth or Decay
X
2
3
4
5
5.
b = _____________
Y
10
9
8.1
7.29
X
0
1
2
3
Growth or Decay
1 𝑥
3
𝑦 =4∙( )
9)
Y
2,500
2,875
3,306.25
3,802.1875
6. Growth or Decay
b = ______________
8)
Y
20
5
1.25
0.3125
3. Growth or Decay
b = ______________
b = _____________
7)
X
0
1
2
3
Y
10
16
25.6
40.96
b = _____________
3 𝑥
2
𝑦 = −2 ∙ ( )
10)
2 𝑥
5
𝑦=( )
Growth or Decay
Growth or Decay
Growth or Decay
Growth or Decay
b = ___________
b = ___________
b = ___________
b = ___________
11. Leah buys a car. Every year the car depreciates in value by 20%.
Growth or Decay
12. Mike's bank account gains 2.3% interest each year.
Growth or Decay
13. Every day, Bradley eats half of the remaining candy in his bag.
Growth or Decay
Find the key information from the graphs of the exponential functions below.
14. Growth or Decay:___________
Domain:___________________
Range:____________________
as 𝑥 → −∞, 𝑓(𝑥) → ____________
as 𝑥 → +∞, 𝑓(𝑥) → ____________
Horizontal Asymptote_________
Y-intercept: ______________
15. Growth or Decay:___________
Domain:___________________
Range:____________________
as 𝑥 → −∞, 𝑓(𝑥) → ____________
as 𝑥 → +∞, 𝑓(𝑥) → ____________
Horizontal Asymptote_________
Y-intercept: ______________
16. Growth or Decay:___________
Domain:___________________
Range:____________________
as 𝑥 → −∞, 𝑓(𝑥) → ____________
as 𝑥 → +∞, 𝑓(𝑥) → ____________
Horizontal Asymptote_________
Y-intercept: ______________