Growth or Decay/ Sequences
Is the following growth or decay: f(x) = 2x
What is growth
Which of the following scenarios best illustrates exponential growth?
A) A person saves $100 in a bank account each month, earning no interest.
B) A tree grows by 2 feet every year, regardless of its size.
C) A population of bacteria doubles every hour under ideal conditions.
D) A car’s value decreases by $1,000 every year.
What is C?
The initial value for the function y = 250(1.2)t.
What is 250?
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
Simplify: (x2)(x3)
x5
Is the following growth or decay: f(x)=100*(0.5)x
What is decay
Which of the following scenarios would best be represented by a linear function?
A) The number of followers on a social media account increases by 10 new followers every day.
B) A virus spreads, doubling the number of infected people every hour.
C) A savings account grows by 5% interest every year.
D) A population of rabbits grows from 100 to 200, then to 400, then to 800 over a few days.
What is A?
The percent of growth for the function y = 250(1.2)t.
What is 20%?
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
Simplify: (2a3b)(4a2b3)
8a5b4
Is the following growth or decay: f(x)=150(1/4)x
What is decay
The equation at this link is which, and why? https://tinyurl.com/5bmss7fa
Exponential because x is an exponent
The percent of decay for the function y = 100(.85)t.
What is 15%?
The population in the town of Huntersville is presently 38,300. The town grows at an annual rate of 1.2%. Write a function, h(x) to model the growth and find the number population of the town after 9 years.
h(x)=38300(1.012)x. Approximately 42,641 people.
Simplify: (3y2)3
27y6
State all the equations that could be used to represent the sequence 6,18,54,162,..., given that a1=6.
A) an=6+12(n-1)
B) an=6(3)n-1
C) an=2(3)n
D) an=12n-6
What are B and C?
The percent of change for the function y =56(0.735)t.
What is 26.5% decay?
The value of a car was $22,000 when it was purchased. They car depreciates at a rate of 19% per year. Write an equation and use it to determine how much will the car be worth in 8 years.
y=22000(0.81)8
$4,076.64
Simplify: (4a)(42)
4a+2
An arithmetic sequence is such that a1=5 and a5=17.
a) State the common difference.
b) Find the 29th term in the sequence.
a) What is 3?
b) What is 89?
The equation A=24,500(0.88)n represents the value of a car n years after it was purchased.
Explain what 24,500 represents in the context of the problem.
What is 24,500 is the initial value of the car?
(5x)(52)y
5x+2y