Linear/Exponential
Growth/Decay?
Growth/Decay?
Is the following linear/exponential and growth/decay: f(x) = 2^x
Exponential Growth
Write an exponential growth function to model the situation. A savings deposit of $3,500 earns 5% for x years.
What is f(x) = 3,500(1+.05)^x
Aunt Mildred invested $10,000 for your college fund in 2006. It earned 2.3% annually. What is the value of the account today?
$15057.80
What is the 50th term of a sequence if the rule is 3n - 2?
148
What is the 6th term in a geometric sequence with a common ratio of -4 and the first term is 2?
-2048
Is the following linear/exponential and growth/decay: f(x)=100*(0.5)^x
Exponential Decay
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
$1,200 is invested at a monthly rate of 3.2%. How much money will the account have after 12 years?
$1576.48
Using the recursive formula below, what is needed to do to find the next term of the sequence? a(n + 1) = a(n) + 18
add 18
What is the common ratio in the sequence .5, 2.25, 10.125, 45.5625?
4.5
Is the following linear/exponential and growth/decay: f(x)= 100-1.4x
Linear Decay
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
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 48,556 People
Write a recursive formula for the following sequence 4, 19, 34, 49,...
a(n + 1) = a(n) + 15,
a(1) = 4
Write a recursive formula for the sequence 1, 6, 36, 216, 1296.
an = 6(an-1)
Is the following linear/exponential and growth/decay: f(x) = 7 (0.94)^x
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
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
Write a recursive formula for the following sequence 3, -9, 27, -81,...
a(n + 1) = (-3)a(n), and
a(1) = 3
A super-ball has a 75% rebound ratio—that is, when it bounces repeatedly, each bounce is 75% as high as the previous bounce. When you drop it from a height of 20 feet, how high does the ball bounce after it strikes the ground for the third time?
8.44 feet
Is the following linear/exponential and growth/decay: f(x) = 5x - 350
Linear Growth
Write an equation to find the balance of an account deposit of $15,000 that earns 4.5% semiannually for x years.
f(x) = 15,000(1+.045/2)^2x
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
Arithmetic or Geometric? Find the next three terms:
-3, 6, -12, 24,...
Geometric. -48, 96, -192
Find the missing terms:
3, _____, 48, 192, _____
12, 768