8.3 Using Accumulation Functions and Definite Integrals in A

A cup of coffee is poured, and the temperature is measured to be 120 degrees Fahrenheit. The temperature of the coffee then decreases at a rate modeled by  $r\left(t\right)=55e^{-0.03t^2}$  
 degrees Fahrenheit per minute, where t
 is the number of minutes since the coffee was poured. What is the temperature of the coffee, in degrees Fahrenheit, at time t=1
 minute?

• 53.4° F

• 54.5°F

• 65.5°F

• 66.6°F

Water is leaking from a dam during a particular week at a rate modeled by the function F given by  $F(t)=5+\frac{t}{4}−\sin\left(\frac{t^2}{5}\right),$  where F(t) is measured in gallons per day and t is the number of days since the start of the week on Sunday. How many gallons of water leak from the dam Tuesday through Thursday, days 2 through 4 ?

• 9.565

• 10.010

• 10.841

• 12.117

The rate at which ants arrive at a picnic is modeled by the function A, where A(t) is measured in ants per minute and t is measured in minutes. The graph of A

for 0≤t≤30 is shown in the figure above. How many ants arrive at the picnic during the time interval 0≤t≤30?

• 8

• 70

• 120

• 140

A ceramic mug is removed from a pottery kiln once the mug reaches a temperature of 700 degrees Celsius. The temperature of the mug then decreases at a rate given by $r\left(t\right)=\frac{20+100\arctan t}{1+t}$  degrees Celsius per minute, where t is the number of minutes since being removed from the kiln. What is the temperature of the mug, to the nearest degree Celsius, at time t=10 minutes?

• 15

• 288

• 412

• 685

Mr. Sullivan can paint his tricycles at a rate of square inches per minute,  $r\left(t\right)=50-\frac{t}{2}$  

where 𝑡 is the number of minutes since he started painting. What is the meaning of  $\int_0^5r\left(t\right)dt$  in the context of this problem 

• The rate at which the square inches are being painted 

• The amount in square pinches are painted during the 5 hours 

• The amount in square pinches are painted during the 5 minutes 

• The amount of paint used in the first 5 minutes 

 A storm has washed away sand from a beach, causing the edge of the water to get closer to a nearby road. The rate at which the distance between the road and the edge of the water was changing during the storm is modeled by  $r\left(t\right)=e^{-\cos t}$  

feet per hour, 𝑡 hours after the storm began. The edge of the water was 80 feet from the road when the storm began. If the storm lasted 5 hours, how far is the water from the road after the storm? 

•  $\int_0^5r\left(t\right)dt$  

•  $80+\int_0^5r\left(t\right)dt$  

•  $80-\int_0^5r\left(t\right)dt$  

•  $5+\int_0^{80}r\left(t\right)dt$  

On a cold winter morning, hot water is pouring into a large container for hot chocolate. The rate 𝑊'(t) at which the water is being poured in the container at time 𝑡,  $0\le t\le10$  

 is shown at selected values in the table above. The cup already had 10 ounces of cold water before pouring the hot water in. Using correct units, interpret the meaning of  $\int_0^3W'\left(t\right)dt\$  in the context of this problem 

• The rate at which the water is being poured in after the first 3 seconds. 

• Total amount of water in the container after the first 3 seconds 

• How much water has been poured into the container during the first three seconds. 

On a cold winter morning, hot water is pouring into a large container for hot chocolate. The rate 𝑊'(t) at which the water is being poured in the container at time 𝑡,  $0\le t\le10$  

 is shown at selected values in the table above. The cup already had 10 ounces of cold water before pouring the hot water in. Use a left Riemann sum, with the five subintervals indicated by the data in the table to Find  $\int_0^3W'\left(t\right)dt\$ 

• 86.2 ounces

• 101.2 ounces

• 75.1 ounces

• 85.1 ounces

On a cold winter morning, hot water is pouring into a large container for hot chocolate. The rate 𝑊'(t) at which the water is being poured in the container at time 𝑡,  $0\le t\le10$  

 is shown at selected values in the table above. The cup already had 10 ounces of cold water before pouring the hot water in. how much water is in the container after 10 seconds?

• 86.2 ounces

• 101.2 ounces

• 75.1 ounces

• 85.1 ounces

The rate at which people arrive at a theater box office is modeled by the function B

, where B(t)

is measured in people per minute and t

is measured in minutes. The graph of B

for 0≤t≤20

is shown in the figure above. Which of the following is closest to the number of people that arrive at the box office during the time interval 0≤t≤20

?

• 15

• 38

• 150

• 188

Tags

CCSS.HSF.IF.B.4