Growth
EXPONENTIAL GROWTH FUNCTION Formula
y=a(l+r)t
EXPONENTIAL DECAY FUNCTION formula
y=a(1-r)t
Exponential functions are defined by an equation of the form _________________.
y=a(b)x
What is the next 3 terms?
4, 8, 16, ________, ________, ________
32,64,128
Annual sales for a fast food restaurant are $650,000 and are increasing at a rate of 4% per year. Use an exponential function to find the annual sales after 7 years.
y=650000(1+.04)7
=855,355.66
The population of a town is 2500 and is decreasing at a rate of 3.5% per year. Use an exponential function to find the population of the town after 5 years.
y=2500(1-.035)5
=2092 people
What does A represent?
What does B represent ?
What does X represent ?
A- initial Value
B-Common Factor
X- input
4 0
1
The population of a school is 800 students and is increasing at a rate of 2% per year. Use an exponential function to find the population of the school after 9 years.
y=800(1+.02)9
=956 students
Daniel’s Print Shop purchased a new printer for $35,000. Each year it depreciates at a rate of 5%. Use an exponential function to find its approximate value after 8 years.
y=35000(1-.05)8
=23,219.72
Linear or exponential ?
y=10x+15
Linear
y=mx+b
46*43
To multiply powers with the same base _____ their exponents.
49
ADD
During a certain period of time, about 70 northern sea otters had an annual growth of 18%. Use an exponential function to find the number of sea otters after 4 years.
y=70(1+.18)4
=135 sea otters
Kathy plans to purchase a car that depreciates at a rate of 12% per year. The initial value of the car is $21,000. Use an exponential function to find the value of the car after 3 years.
y=21000(1-.12)3
=14,310.91
Linear or Exponential?
y=-5(16)10
Exponential
To divide powers with the same base ______ their exponents.
46/43
Subtract
43
Twenty years ago, Mr. Davis purchased his home for $160,000. Since then, the value of the home has increased about 5% per year. Use an exponential function to find the value of the home today
y=160000(1+.05)20
=424,527.63
A population of fish starts at 8,000 and decreases by 6% per year. Use an exponential function to find the population of fish in 10 years.
y=8000(1-.06)10
4308 fish
How can you tell if a graph is linear?
How can you tell if a graph is exponential?
Linear-Straight line
Exponential-Curved line
To fins a power of a power ____ the exponents.
(46)3
multiply
418