A pizza buffet has prepared 20 pizzas to place on the line at the beginning of lunch at 11:00 a.m. The equation used to describe the total number of pizzas that have been placed out on the buffet line is shown below.
If x represents every 8 minutes after
Every 16 minutes, 32 more pizzas were set out on the buffet.
A pizza buffet has prepared 22 pizzas to place on the line at the beginning of lunch at 11:00 a.m. The equation used to describe the total number of pizzas that have been placed out on the buffet line is shown below.
y= 18x + 22
If x represents every 6 mi
Every 12 minutes, 36 more pizzas were set out on the buffet.
Using the graph above, determine at which of the following values of x is the rate of change of the function close to 1.
0
The graph shows the distance a car can travel, d, on g gallons of gasoline. How many miles per gallon does the car get?
25 miles per gallon
The function below represents the balance of a savings account, which is compounded continuously at an annual interest rate, t years after an initial deposit of $9,000.
A(t) = $9,000e0.06t
What is the approximate average rate of change over the interval [
$850.07 per year
The function below represents the balance of a savings account, which is compounded continuously at an annual interest rate, t years after an initial deposit of $2,000.
A(t) = $2,000e0.08t
What is the approximate average rate of change over the interval [
$293.49 per year
Audrey opened a boutique in her neighborhood. Her profit, in dollars, over a period of seven years is given by the function below.
What is the average rate of change over the interval [3, 7]?
$7,575 per year
The number of views of a viral video is increasing at an exponential rate. The table represents the number of views of the video after x hours.
x 3 5 7 9 11
g(x) 27 243 2,187 19,683 177,147
What is the average rate of change over the interval [5, 9]?
4,860 views per hour
The graph shows the population, p, of a town after t years have elapsed. What is the annual rate of growth in the town?
2,500 people per year
Cesar needs cups of flour to make a cake that will serve 16 people. If Cesar wants to make enough cake to serve 32 people, how many cups of flour will he need?
2 1/2
The graph represents the value of a car after x years from the date of purchase.
Estimate the average rate of change over the interval [2, 8].
-$1,000 per year
Peter made an initial deposit into a savings account that accrues interest annually. The table represents the amount of money in his savings account in x years
x 4 9 14 19 24
g(x) $4,081.47 $5,997.01 $8,811.58 $12,947.10 $19,023.54
What is the approximate
$591.04 per year
A fighter jet reaches the maximum point of elevation for its flight path 70 miles after take-off. The equation used to determine the total number of miles the jet will travel is shown below.
If y represents the total number of miles traveled, and x repres
For every 1 minute flying at maximum elevation, the fighter jet will travel an additional 7 1/2 miles.
The graph above shows the amount Tina earns, w, before taxes after working h hours. How much does Tina make per hour?
$8.00
Using the graph above, determine at which of the following values of x is the rate of change of the function close to -4.
-3
Observe the three exponential functions below, each one expressed as a graph, table, or equation.
Put the functions, with their corresponding intervals, in order from least to greatest according to their average rates of change over those intervals.
f(x) interval [2,3]; h(x) interval [2,3]; g(x) interval[2,4]; h(x) interval [3,4]
Scientists are examining a substance that has a half-life of 10 years. The table represents the amount, in grams, of the substance after x half-life cycles.
x 2 3 4 5 6
g(x) 750 375 187.5 93.75 46.875
What is the average rate of change over the interval [
-70.31 grams per half-life cycle
Astrid has a data plan through her cell phone company where she pays $44 a month for 5,000 kilobytes (KB) of data and $0.025 for each additional KB over 5,000. To the nearest cent, how much would Astrid need to pay for her data plan if she used 5,673 KB o
$60.82
Josh is going on a road trip to the country side. The table represents the distance, in miles, Josh has traveled after x hours.
x 2 5 8 11 14 17
g(x) 118 295 472 649 826 1,003
What is the average rate of change over the interval [8, 17]?
59 miles per hour
Peter made an initial deposit into a savings account that accrues interest annually. The table represents the amount of money in his savings account in x years
x 2 7 12 17 22
g(x) $3,244.80 $3,947.80 $4,803.10 $5,843.70 $7,109.76
What is the approximate a
$173.26 per year
The graph shows the cost, C, of sending m text messages. What is the cost per message?
$0.15 per message
An amusement park issued a coupon to increase the number of visitors to the park each week. The function below represents the number of visitors at the amusement park x weeks after the issuance of the coupon.
V(x) = 600(1.5)x
What is the approximate avera
1,371 visitors per week
Michael got a job peeling potatoes. In the first two hours of his shift, he peeled 48 potatoes. How many potatoes can he peel in eight hours?
192
Michael got a job peeling potatoes. In the first two hours of his shift, he peeled 52 potatoes. How many potatoes can he peel in eight hours?
208
Michael got a job peeling potatoes. In the first two hours of his shift, he peeled 60 potatoes. How many potatoes can he peel in nine hours?
270
In Ben's apartment complex, residents are fined $15 per day each day the rent is late. Last month, Ben wrote the apartment complex a check for $1,040 when his monthly rent is only $845. How many days late was Ben's rent?
13
A factory manufactures handbags. The number of handbags it manufactures per hour on a certain day is given by the table below.
Time (hours)
x Number of Handbags
f(x)
0 0
1 25
2 50
3 75
4 100
5 125
6 150
7 150
8 190
9 230
10 270
What is the average rate of
30 handbags per hour
Patrick made tortilla soup in his slow cooker and has turned the heat off to allow the soup to cool slightly before consuming. The temperature, in degrees Fahrenheit, of the soup x minutes after the heat was turned off is represented by the function below
-2.44 degrees per minute
A fighter jet reaches the maximum point of elevation for its flight path 50 miles after take-off. The equation used to determine the total number of miles the jet will travel is shown below.
y= 18 1/3x + 50
If y represents the total number of miles travel
For every 1 minute flying at maximum elevation, the fighter jet will travel an additional 18 1/3 miles.
The graph represents the number of subscribers for a mobile company x months from the start of operations.
Estimate the average rate of change over the interval [5, 10].
340 subscribers per month
The number of graduating seniors at two local high schools is shown in the graphs, where x represents the number of years since 2005. The number of students graduating from Fannon High School is represented by f(x), and the number of students graduating f
From 2005 to 2010, the average increase of the number of graduating seniors per year is greater for
fannon
High School than for
guthrie
High School by
50
students per year.
Megan is going on a long distance road trip. She drives for 19 miles before being able to travel at a constant speed using cruise control. The equation used to find her total distance traveled is shown below.
y=70x + 19
If y is the total number of miles d
For every hour, she will drive 70 miles.
Josh is going on a road trip to the country side. The table represents the distance, in miles, Josh has traveled after x hours.
x 2 5 8 11 14 17
g(x) 102 255 408 561 714 867
What is the average rate of change over the interval [8, 17]?
51 miles per hour
During the holiday season, Duke and Iris work at a gift-wrapping station. Duke can wrap 49 gifts per hour, and Iris can wrap 38 gifts per hour. If they work together, how long will it take them to wrap 435 gifts?
5 hours
The graph represents the value of an investment account x years from the date of the initial investment.
Estimate the average rate of change over the interval [15, 25].
$1,800 per year
Rick's Truck Rentals provides a one-day rental charge represented by the function below, where x represents the number of miles driven.
R(x)= $0.60x +$20
What is the average rate of change over the interval [180, 240]?
$0.60 per mile
Adelaide has a credit card with a company that charges $2.50 for every day a payment is late. If she paid $548.56 for a bill that is 3 days late, how much was the bill without the late fee?
$541.06
A software company developed a mobile application to help students stay organized. The table represents the number of downloads of the application x days after its release date.
x 20 40 60 80 100 120
g(x) 3,534 6,654 9,774 12,894 16,014 19,134
What is the
156 downloads per day
The graph represents the coyote population in a town x years from the date of their initial discovery.
Estimate the average rate of change over the interval [35, 70].
11 coyotes per year
Landry has made 1,267 cups of coffee with her coffeemaker, and she has changed the reusable filter 6 times. She needs to change the filter again and wants to know how many cups of coffee she can make using the new filter. If the coffeemaker came with one
181
The graph shows the altitude, a, of a plane, in feet, after t minutes. What is the rate of ascent of the airplane?
125 feet per minute
To get to work, Truman waited 14 minutes for the bus, then traveled 22.4 miles on the bus at a speed of 32 miles per hour. How much time passed from the time Truman left for work to the time he arrived at work?
56 minutes
While riding in a car, Rachel saw 14 red cars pass by in one minute. At this rate, how many red cars will she see in 2 hours?
1,680
A water-storage tank is being emptied for cleaning. The amount of water left in the tank, in liters, is represented by the function below, where x represents the time elapsed, in minutes.
W(x)= -12x + 60
What is the average rate of change over the interva
-12 liters per minute
Tara is training for a marathon. She is able to run 6 miles before settling into a constant pace. The equation to find her distance after her pace is set is shown below.
y= 5/27x +6
If y is the total miles run, and x is the number of minutes after she rea
For every minute, she will run of a mile.