Growth or Decay?
Applying Exponential Equations
Initial Amount, Growth Factor, and Growth Rate
Writing Exponential Functions
Negative and Zero Exponents
100
Is the following growth or decay: f(x) = 2^x
What is growth
100
The population in the town of Huntersville is presently 38,300. The town grows at an annual rate of 1.2%. Find the number population of the town after 9 years.
Approximately 42,640 people
100

Use y = 250(1.2)^t What is the initial value?

What is 250

100

Write an exponential growth function to model the situation. A population of 422,000 increases by 12% each year.

What is f(x) = 422,000(1.12)^x

Bonus- If this was continuous growth, what would the equation be?

100
Simplify: 6tv^0
6t
200
Is the following growth or decay: f(x)=100*(0.5)^x
What is decay
200
$1,200 is invested at an annual rate of 3.2%. How much money will the account have after 12 years?
$1751.21
200
Use y = 250(1.2)^t What is the growth factor?
What is 1.2
200
How can you tell from a table that you are dealing with an exponential function?

How do you write an equation of an exponential function by looking at a table?

the y values shows a multiplying pattern

y = ab^x where a is from (0, a) and the b value is what the y values multiply by every time the x value increases by one.

200
Simplify: (4^2)(x^(-2))
8 / x^2
300
Is the following growth or decay: f(x)= 100*(1.4)^x
What is growth
300
The population in the town of Deersburgh is presently 42,500. The town has been growing at a steady rate of 2.7%. What will the population of the town be in 5 years?
Approximately 42, 499 People
300

Use y = 250(1.2)^t What is the growth rate? (Expressed as a percent)

What is 20%

300

The Hippityhoppity bunny decided to have a family reunion at the Magic Forest every 5 years. During the second reunion the family discovered that the number of family members was 154 and was growing at an annual rate of 3.2%. Write an equation to model the growth of the bunny family.

What is f(x) = 154(1.032)^x

Bonus- if this were continuous growth what would the equation be?

300
Simplify: 4(x^-2)(g^3)
4g^3 / x^2
400
Is the following growth or decay: f(x) = 7 (0.94)^x
What is decay
400
The value of a car was $22,000 when it was purchased. They car depreciates at a rate of 19% per year. How much will the car be worth in 8 years?
$4,076.64
400
y = 9.8(1.35)^t What is the growth factor?
What is 1.35
400

The fish in The Magic Forest Lake were declining at an annual rate at 1.5%. Their current number is estimated at 2500. Write an equation to model the decreasing number of fish.

What is y = 2500(.985)^x

400
Simplify: ( (4^-2)(x^-5)(y^-9)(z^-3) )^0
1
500
Is the following growth or decay: f(x) = -350 (1.25)^x
What is growth
500
The value of a stock when purchased is $10 a share. However, over the past 5 days the price went down at a constant rate of 4%. How much is the stock worth now?
$8.15
500

y = 9.8(1.35)^t What is the growth rate? (Expressed as a percent)

What is 35%

500

The squid in The Magic Forest Lake were declining at an annual rate at 5.5%. Their current number is estimated at 50,000. Write an equation to predict the number of squid in the lake in 10 years.

What is f(10) = 50000(.945)^10 and 28,398 squid

500
( (x^-2)(y^2) ) / ( (b^-4)(c^4) )
( (b^4)(y^2) ) / ( (c^4)(x^2) )
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