Linear, Exponential, or Neither
Is the relationship linear, exponential, or neither?
x: 0, 1, 2, 3
y: 4, 8, 16, 32
Exponential
For which function does f decrease by 12% every time x increases by 1?
A. f(x) = 0.12^x
B. f(x) = 12^x
C. f(x) = 0.88^x
D. f(x) = 1.12^x
C. f(x) = 0.88^x
The expression 8(1.05)^t represents the amount of money, in thousands of dollars, in an account after t years.
What does the 8 represent?
A. The account increases by 8% each year.
B. The account started with $8,000.
C. The account doubles every 8 years.
D. The account was opened 8 years ago.
B. The account started with $8,000.
A game starts with 10 points. Each round has 3 times as many points as the previous round.
Which equation shows the number of points, p, in round n?
A. p = 10 + 3n
B. p = 3(10)^n
C. p = 10(3)^n
D. p = 10n + 3
C. p = 10(3)^n
Simplify.
√36
6
Is the relationship linear, exponential, or neither?
x: 0, 1, 2, 3
y: 1, 4, 9, 16
neither
A population of bacteria starts at 500 and doubles every hour.
Which expression represents the population after t hours?
A. 500 + 2t
B. 500(2)^t
C. 2(500)^t
D. 500(0.5)^t
B. 500(2)^t
The expression 250(1.07)^t models the number of people at an event after t years.
What does 1.07 represent?
A. The amount decreases by 7% each year.
B. The amount increases by 7% each year.
C. The starting amount is 107 people.
D. The amount increases by 107 each year.
B. The amount increases by 7% each year.
A plant is 6 inches tall and grows by 9% each week.
Which function represents the height, h, after w weeks?
A. h = 6(1.09)^w
B. h = 6(0.09)^w
C. h = 6 + 9w
D. h = 9(6)^w
A. h = 6(1.09)^w
Simplify. Remove all perfect squares from inside the square root.
√48
4√3
Is the relationship linear, exponential, or neither?
x: 0, 1, 2, 3
y: 5, 9, 13, 17
Linear
A car loses 15% of its value each year.
If the car is worth $18,000 now, which expression represents its value after t years?
A. 18,000(1.15)^t
B. 18,000(0.15)^t
C. 18,000(0.85)^t
D. 18,000 + 15t
Function B
C. 18,000(0.85)^t
The expression 600(0.92)^t models the value of a laptop after t years. What does 0.92 represent?
A. The laptop increases by 92% each year.
B. The laptop decreases by 92% each year.
C. The laptop keeps 92% of its value each year.
D. The laptop started at $920.
C. The laptop keeps 92% of its value each year.
A membership starts with 400 people and decreases by 10% each year.
Which function represents the membership, m, after t years?
A. m = 400(1.10)^t
B. m = 400(0.90)^t
C. m = 400 - 10t
D. m = 10(400)^t
B. m = 400(0.90)^t
Simplify.
√75
5√3
The number of students participating in a club increases by 6% each year.
Which kind of function best models this relationship?
A. Linear
B. Exponential
C. Neither
B) Exponential
For which function does f increases by 12% every time x increases by 1?
A. f(x) = 0.12^x
B. f(x) = 12^x
C. f(x) = 0.88^x
D. f(x) = 1.12^x
D. f(x) = 1.12^x
The function c(x) = 45(1.03)^x models the cost of a museum ticket, in dollars, x years after 2024.
Which year is represented by x = 6?
A. 2024
B. 2025
C. 2026
D. 2030
D. 2030
A video is shared with 5 people. Each day, the number of people who see the video is multiplied by 4.
Which expression shows the number of people who see it after d days?
A. 5 + 4d
B. 4(5)^d
C. 5(4)^d
D. 20d
C. 5(4)^d
Simplify the rational expression.
(8x + 4) / (12x + 6)
A. 2/3
B. (2x + 1)/(3x + 1)
C. (4x + 2)/(6x + 3)
D. Cannot be simplified
A. 2/3
A phone loses the same 8% of battery power every hour.
Which kind of function best models the relationship between time and battery power?
A. Linear
B. Exponential
C. Neither
A) Linear
A town's population increases by 4% each year.
If the current population is 75,000, which expression represents the population after 5 years?
A. 75,000(1.04)^5
B. 75,000(0.04)^5
C. 75,000 + 1.04(5)
D. 75,000(1.05)^4
A. 75,000(1.04)^5
The expression 12(0.75)^t represents the amount of medicine, in milligrams, remaining in the body after t hours.
What does the expression show?
A. The medicine increases by 75% each hour.
B. The medicine decreases by 25% each hour.
C. The medicine decreases by 75% each hour.
D. The medicine starts with 75 milligrams.
B. The medicine decreases by 25% each hour.
A bank account begins with $1,200 and earns 2.5% interest each year.
Which expression represents the amount after t years?
A. 1,200(2.5)^t
B. 1,200(0.25)^t
C. 1,200(1.025)^t
D. 1,200 + 2.5t
C. 1,200(1.025)^t
The cost of a chemical is modeled by
c(x) = 80(1.05)^x.
x represents the number of years since 2015.
About how much will the chemical cost in 2020?
A. $84.00
B. $97.22
C. $102.10
D. $105.00
2020 is 5 years after 2015.
80(1.05)^5 ≈ 102.10