Geometric Sequences
What is the common ratio, r, of the following sequence 1, 4, 16, 64,...
r = 4
Does an exponential function add/subtract or multiply/divide from term to term?
multiply/divide
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
Is the following growth or decay: f(x) = 2^x
What is Growth
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
What is the common ratio, r, of the following sequence -3, 6, -12, 24,...
r = -2
Is the graph of an exponential function linear or curved (non-linear)?
Curved (non-linear)
The population of Baconburg starts off at 20,000, and grows by 13% each year. Write an exponential growth model and find the population after 10 years.
What is f(10) = 20,000(1.13)^10 and population of 67,891
Is the following growth or decay: f(x)=100*(0.5)^x
What is Decay
$1,200 is invested at an annual rate of 3.2%. How much money will the account have after 12 years?
$1751.21
what is the 6th term of the following sequence if the rule is: a(n) = 4(3)n
2916
Does the following equation represent an exponential growth or decay? f(n) = 112(1.5)n
Exponential Growth
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
Is the following growth or decay: f(x)= 100*(1.4)^x
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
Find the explicit equation of the following sequence 20, 10, 5, 2.5,...
a(n) = 40(.5)n
Does the following equation represent an exponential growth or decay? f(n) = 112(.5)n
Exponential Decay
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
Is the following growth or decay: f(x) = 7 (0.94)^x
What is Decay
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
t(2) = 20 and t(3) = 80
Find the explicit equation of this geometric sequence.
t(n) = 1.25(4n)
Tony started with 2 bunnies and each month each pair of bunnies will have 8 babies! Write the exponential equation that can be used to find the number of bunnies at the end of any month.
y = 2(5n)
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
Is the following growth or decay: f(x) = -350 (1+0.25)^x
What is Growth
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