Module 5 Vocabulary
Growth or Decay Part 1
Growth or Decay Part 2
Word Problems
Sequences
100
If, y=a(b)x, What do a and b represent?
a=initial amount/y-intercept
b=multiplier (common ratio)(growth or decay factor)
100
How do I know if an exponential function is exponential decay from an equation?
If the b is in between 0 and 1
100
A bunny population doubles every year. If the starting population is 10, write an exponential function to model the situation.
f(x)= 10(2)x
100
2243
100
Find the next three terms in this sequence:
0, 3, 8, 15, 24.....
35, 48, 63
200
What refers to the constant percentage increase that a quantity grows over equal time intervals?
Growth Rate
200
f(x) = 4(0.8)x
What is the percent of decay?
20% decay
200
In exponential functions, when b>1 this will cause an exponential growth or decay?
Exponential growth
200
What will be the cost in 17 years?
$32,313.27
200
Write a recursive formula for the following sequence:
14, 21, 28, 35
f(n)=f(n-1)+7
300
What is the difference between simple and compound interest?
Simple interest is calculated only on the initial principal amount, resulting in steady, linear growth. Compound interest is calculated on the principal plus previously accumulated interest, leading to faster, exponential growth over time.
300
What is the equation for the graph below?
y = 1•2^x
300
f(x)=5(1.07)x
Does this functions represent exponential growth or decay? What's the percent growth/decay factor?
Exponential Growth. 7%.
300
Ms. Wiggins purchased a car for 26,400 and every year it decays by 12%. Write an exponential function to model the situation.
f(x) = 26,400(0.88)x
300
Find the first five terms in the following sequence:
for n>1 where f(0) =4
4, 6, 9, 27/2, 81/4
400
What is the difference between linear functions and Exponential functions?
Linear has a constant difference (constant rate of change)
Exponential has a constant multiplier
400
Write an exponential function that goes through the points (0, 3.5) and (2, 31.5)
y=3.5(3)x
400
Annual sales of a fast food restaurant are $530,000 and increasing at a rate of 5%. Write an exponential function to model the situation.
f(x) = 530,000(1.05)x
400
16,941 people
400
N, A, G, G, A
500
What is the difference between a recursive and an explicit formula?
Recursive formulas define a sequence by relating each term to previous ones, requiring the first term to start. Explicit formulas define terms directly based on their position n
500
Consider the function
What is the value of each:
f(x)=10x
1. f(x+1) - f(x)
2.
(f(10)-f(1))/(10-1)
3.
f(x+1)/f(x)
1. 10
2. 10
3. 10x+10/10x
500
A new phone sells for $899. The value of the phone will decrease 46.4% each year after it is sold.
Write an equation AND find the after 3 years.
f(x)=899(0.536)^x
3 years = 138.44
500
Find the average rate of change for both towns on the interval 0<t<10
Town A: 360
Town B: 360
500
Mr. Novak receives a bonus at the end of each year of employment. The amount of the bonus each year is represented by the sequence shown.
1200, 1320, 1452, 1597.20, …
Write a recursive formula
