Write the expression
What does the 1.05 mean in f(x)=300(1.05)^3 mean?
A population starts at 100,000 and grows by 3% each month.
Write the correct expression for the population after 3 months.
** number 1 on review
y = 100,000(1.03)3
f(x)=5(1.02)x
Increasing by 2 percent
A credit card charges 24% interest each year, compounded twice a year (every 6 months).
What percent would you use in your equation?
1.12 --> 12%
Which one grows faster? Why?
f(x)=50(1.05)x and g(x)=50(1.10)x
g(x) grows faster because 10% > 5%, and exponential growth compounds over time.
A population starts at 200 and increases 5% per year.
P(x)=200(1.05)x
A library starts with 5,000 books and grows by 2% each month.
Write an expression for the number of books after 36 months (in thousands).
**number 2 on review
y = 5(1.02)36
f(x)=30(0.9)x
Decreasing by 10 percent
A credit card charges 24% interest each year, compounded twice a year (every 6 months). If a person spends $2000 and makes no payments and no additional charges, what is the balance on the credit card after 3 years?
What would the exponent be in this equation?
6 (2 times a year times 3 years)
The function c(x)=5(1.02)x represents the cost in dollars, c, for a restaurant to prepare a pot of soup. x represents the number of months that they have been making this soup.
Does the cost of the soup increase or decrease over time, and by what percentage per month does it do so?
** number 7a on review
Increase by 2%
A value starts at 50 and decreases 12% each year.
V(x)=50(0.88)x
Which function increases by 10% each time x increases by 1?
A. f(x)=1.1x
B. f(x)=1.9x
C. f(x)=90x
D. f(x)=10x
** number 3 on review
A. f(x)=1.1x
f(x)=10(0.95)x
Decreasing by 5 percent
A student puts $1,500 into a savings account that earns 8% annual interest, compounded quarterly.
What will the account balance be after 2 years?
1500(1.02)8 = $1757.49
The function c(x)=5(1.02)x represents the cost in dollars, c, for a restaurant to prepare a pot of soup. x represents the number of months that they have been making this soup.
How much does a pot of soup cost to make after 8 months? Show your reasoning.
** number 7b on review
5(1.02)8=$5.86
A value starts at 80 and increases 15% each period.
y=80(1.15)x
Write function g showing a decrease by 7% each time x increases by 1.
Write the function.
**number 4 on review
f(x)=(0.93)x
f(x)=12(1.08)x
Increasing by 8 percent
Find and correct the mistake.
$2000 invested with a yearly nominal interest rate of 9% compounded quarterly for 2 years.
Work:
f(x)= 2000(1.09)8
They did not compound the interest rate. They should have taken 0.09 and divided by 4 to get 0.0225.
Correct work: 2000(1.0225)8
You’re opening a new bank account. You have $500 to deposit, and you are not planning to withdraw or deposit any more money for 8 years. You are choosing between these 2 options:
Option 1: An account that grows by 11% each year.
Option 2: An account that grows by $100 each year.
Which option will result in a larger balance? Explain your reasoning.
**number 9 on review
Option 2.
500(1.11^8) = $1152.27
500+8(100) = $1300
A value starts at 120 and decreases 3% each period.
y=120(0.97)x
You start with 4 dollars. A quantity triples every time x increases by 1. Write the function.
f(x)=4(3)x
Increasing or decreasing?
f(x) = 47(0.08)x
By what percentage per year?
What would the function equal when x is 3?
** number 6 on review
Decreasing by 92%. f(3)=0.024064
A credit card charges 24% interest each year, compounded twice a year (every 6 months). If a person spends $2000 and makes no payments and no additional charges, what is the balance on the credit card after 3 years?
** number 5 on review
$3947.65
The graph represents the function g(x)=3.75693x. The coordinates for point A are (2, c) and the coordinates for point B are (5, d). What is the value of d/c?
**number 8 on review -- see image on paper
27 → plug the first value of x (2) into the function to get c=33.8121 and then plug the second x value (5) into the function to get d= 912.9267. Divide the value of d by the value of c. Or, look at the growth factor of 3: since x increases by 3, you would have 33=27.