Growth or Decay?
Does this function represent growth or decay?
Identify a and b.
f(x)=2^x
What is growth?
The population in the town of Gainesville is presently 38,300. The town grows at an annual rate of 1.2%.
Write an exponential function to predict the population after x years.
Find the expected population of the town in 9 years.
What is approximately 42,641 people
Identify the initial value of this function:
f(x)=250(1.2)^x
Initial Value (a) = 250
Write an exponential function to model the situation.
A population of 422,000 increases by 12% each year.
f(x)=422,000(1.12)^x
Identify the growth/decay factor:
Increase by 3%
Growth Factor:
1.03
Does this function represent growth or decay?
Identify a and b.
f(x)=100(0.5)^x
What is decay?
$1,200 is invested at an annual rate of 3.2%, compounded annually.
Write an exponential function to predict the total amount of money after x years.
How much money will be in the account after 12 years?
$1751.21
Identify the growth factor of this function:
f(x)=250(1.2)^x
Growth Factor (b) = 1.2
Write an exponential function to model the situation.
The population of Baconburg starts off at 20,000, and grows by 13% each year.
f(x)=20,000(1.13)^x
Identify the growth/decay factor:
Decrease by 7%
Decay Factor:
0.93
Does this function represent growth or decay?
Identify a and b.
f(x)=100(3/2)^x
What is growth
The population in the town of Battlesburg is presently 42,500. The town has been growing at a steady rate of 0.6%.
Write an exponential function to predict the population after x years.
What is the expected population of the town in 5 years?
Approximately 43,790 People
What percent growth does this function represent?
f(x)=250(1.2)^x
This function represents a 20% growth.
Write an exponential function to model the situation.
During a study of ptarmigan it was found that the population in one area was 154 and was growing at an annual rate of 3.2%.
f(x)=154(1.032)^x
Identify the growth/decay factor:
Increases by 90%
Growth Factor:
1.90
Does this function represent growth or decay?
Identify a and b.
f(x)=7(0.94)^x
What is decay
The value of a car was $22,000 when it was purchased. The car depreciates at a rate of 19% per year.
Write an exponential function to predict the value of the car after x years.
How much will the car be worth in 8 years?
$4,076.64
There are currently 5 strands of bacteria living in petri dish. It is said to decrease by 7% every day.
Identify the the decay factor (b)?
Decay Factor (b) = .93
Write an exponential function to model the situation.
The current number of fish in The Magic Forest Lake was estimated at 2500 and is declining at an annual rate of 8%.
f(x)=2500(.92)^x
Identify the growth/decay factor:
Loses 17%
Decay Factor:
0.83
Does this function show growth or decay: f(x) = 350 (1.25)^x
Does this function represent growth or decay?
Identify a and b.
f(x)=350(1.25)^x
What is growth
The value of a stock when purchased is $1000 a share. The stock started to decline in value by 4% each year.
Write an exponential function to predict the value of the stock after x years.
How much is the stock worth after 3 years?
$884.74
What percent decay does this function represent?
f(x)=9.8(0.76)^x
This function represents a 24% decay.
Write an exponential function to model the situation.
The population is said to be 154,000 squid in The Magic Forest Lake. The population is getting cut in half every year.
f(x)=154,000(0.5)^x
Identify the growth/decay factor:
Grows by 22%
Growth Factor:
1.22