Using Formulas
To rent a carpet cleaner at the hardware store, there is set fee and an hourly rate. The rental cost, c, can be determined using this equation when the carpet cleaner is rented for h hours.
c = 25 + 3h
Which of these is the hourly rate?
A) 3 B) 3h C) 25 D) 25h
A) 3
To rent a canoe, the cost is $3 for the oars and life preserver, plus $5 an hour for the canoe. Which graph models the cost of renting a canoe?
C
I bought a car for $25,000, but its value is depreciating at a rate of 10% per year. How much will my car be worth after 8 years?
25,000(0.9)^8 = 10,761.68025
$10,761.68
A ball is shot from a cannon into the air with an upward velocity of 40 ft/sec. Find the starting height of the ball. The equation that gives the height (h) of the ball at any time (t) is:
h(t) = -16t^2+40t+2
2 feet
For what value of x is the inequality 2/3 + x/3 > 1 true?
A) x < 1 B) x > 1 C) x < 5 D) x > 5
B) x > 1
This equation can be used to find h, the number of hours it will take Flo and Bryan to mow their lawn.
h/3 + h/6 = 1
How many hours will it take them to mow their lawn?
A) 6 hours B) 3 hours C) 2 hours D) 1 hour
C) 2 hours
Juan and Patti decided to see who could read more books in a month. They began to keep track after Patti had already read 5 books that month. This graph shows the number of books Patti read for the next 10 days and the rate at which she read for the rest of the month.
If Juan does not read many books before day 4 and he starts reading at the same rate as Patti for the rest of the month, how many will he have read by day 12?
A) 5 B) 10 C) 15 D) 20
B
You deposit $1500 in an account that pays 5% interest compounded yearly. Find the balance after 6 years.
1500(1.05)^6 = 2,010.143461
$2010.14
A ball is shot from a cannon into the air with an upward velocity of 40 ft/sec. Find the maximum height of the ball. The equation that gives the height (h) of the ball at any time (t) is:
h(t) = -16t^2+40t+2
27 feet
If the parent function f(x) = mx + b, what is the value of the parameter m for the line passing through the points (-2, 7) and (4, 3)?
A) -9 B) -3/2 C) -2 D) -2/3
D)
The expression s2 is used to calculate the area of a square, where s is the side length of the square. What does the expression (8x)2 represent?
A) the area of a square with a side length of 8
B) the area of a square with a side length of 16
C) the area of a square with a side length of 4x
D) the area of a square with a side length of 8x
D) the area of a square with a side length of 8x
The function graphed on this coordinate grid shows f(x), the height of a dropped ball in feet after its xth bounce.
On which bounce was the height of the ball 10 feet?
A) 1 B) 2 C) 3 D) 4
A
A certain population of bacteria has an average growth rate of 2%. The formula for the growth of the bacteria is A = P0 * 1.02t, where P0 is the original population and t is the time in hours.
If you begin with 200 bacteria, about how many bacteria will there be after 100 hours?
A) 7 B) 272 C) 1,478 D) 20,000
C) 1,478
An object is thrown in the air with an initial velocity of 5 m/s from ta height of 9 m.
The equation h(t) = -4.9t2 + 5t + 9
models the height of the object in meters per second.
About how many seconds does it take for the object to hit the ground?
A) .94 seconds B) 1.50 seconds
C) 2 seconds D) 9 seconds
C) 2 seconds
A shop sells one-pound bags of peanuts for $2 and three-pound bags of peanuts for $5. If 9 bags are purchased for a total cost of $36, how many three-pound based were purchased?
A) 3 B) 6 C) 9 D) 18
B) 6
Sandra sells necklaces at a school craft fair. She uses the equations P = 7.5n - (2.25n +15) to determine her total profit at the fair. Based on this equation, how much does she charge for each necklace?
A) $2.25 B) $7.50 C) $15.00 D) $17.25
B) $7.50
The graph shows the height, y, in meters, of a rocket above sea level in terms of the time, t, in seconds, since it was launched. The rocket landed at sea level.
Describe what the x-intercepts represent for this situation.
The time it took the rocket to return to the ground.
You deposit $98,000 in an account in 2005 that pays 11% interest compounded semiannually. Find the balance in 2021.
98,000(1+.11/2)^(2*16) = 543,631.7135
$543,631.71
A diver is standing on a platform 24 ft. above the pool. He jumps form the platform with an initial upward velocity of 8 ft/s. Find the time that the diver will be 16ft in the air. The equation that gives the height (h) of the diver at any time (t) is:
h(t) = -16t^2+8t+24
1 second
Which statement is FALSE?
f(x) = -2(3)x-1 +5
A) exponential growth that reflects over the x-axis
B) asymptote at y = 5
C) vertical shrink, shifts right 1 and up 5 units
D) all statements are true
C
A manager is comparing the cost of buying baseball caps from two different companies.
-Company X chargers a $50 fee plus $7 per cap
-Company Y charges a $30 fee plus $9 per cap
For what number of baseball caps will the cost be the same at both companies?
A) 10 B) 20 C) 40 D) 100
A) 10 baseball caps
The population of squirrels doubles every year. Initially, there were 5 squirrels. A biologist studying the squirrels creates a function to model their population growth:
P(t) = 5(2)t, where t is the time in year. The graph of the function is shown.
What is the range of the function?
A) any real number
B) any whole number greater than 0
C) any whole number greater than 5
D) any whole number greater than or equal to 5
D) any whole number greater than or equal to 5
A sample of 1,000 bacteria becomes infected with a virus. Each day, one-fourth of the bacteria sample dies due to the virus. A biologist studying the bacteria models the population of the bacteria with the function P(t) =1,000(0.75)t, where t is the time, in days.
What is the range of this function in this context?
A) any real number such that t > 0
B) any whole number such that t > 0
C) any real number such that 0 < P(t) < 1,000
D) any whole number such that 0 < P(t) < 1,000
D) any whole number such that 0 < P(t) < 1,000
The expression below represents a company's profit for selling x items. For where number(s) of items sold is the company's profit equal to $0?
A) 0 B) 35 C) 10 & 60 D) 20 & 30
-x^2+70x-600
C) 10 & 60 items
A cafe's annual income depends on x, the number of costumers. The function I(x) = 4x2 - 20x describes the cafe's total annual income. The function C(x) = 2x2 +5 describes the total amount the cafe spends in a year. The cafe's annual profit, P(x), is the difference between the annual income and the amount spent in a year.
Which function describes P(x)?
A) P(x) = 2x2 - 20x - 5
B) P(x) = 4x3 - 20x2
C) P(x) = 6x2 - 20x + 5
D) P(x) = 8x4 - 40x3 - 20x2 - 100x
A) P(x) = 2x2 - 20x - 5