Integrating Real-World Problems: Average Values & Distance

A car travels along a straight road, and its speed is given by the function v(t) = 4t + 2, where t is in hours. Find the total distance traveled by the car from t = 1 to t = 3 hours.

• 18

• 20

• 15

• 25

The area under the curve of the function f(x) = 3x^2 from x = 0 to x = 2 represents the total amount of paint needed to cover a wall. Calculate the area.

• 8

• 4

• 10

• 6

A farmer wants to find the average height of his corn plants over a growing season. The height of the plants can be modeled by the function h(t) = 2t^2 + 3t, where t is in weeks. Find the average height from week 1 to week 5.

• 15

• 25

• 40

• 31

A water tank is being filled at a rate modeled by the function r(t) = 5t + 10 liters per hour. How much water is in the tank after 4 hours?

• 100 liters

• 60 liters

• 40 liters

• 80 liters

The temperature of a substance is modeled by the function T(t) = 20 + 10sin(t), where t is in hours. Find the average temperature of the substance over a 2-hour period.

• 25.54

• 22.10

• 30.00

• 15.75

A cyclist travels along a path where their speed is given by s(t) = 6t - 1. Calculate the total distance traveled by the cyclist from t = 0 to t = 5 seconds.

• 50

• 70

• 60

• 80

The revenue generated by a small business can be modeled by the function R(x) = 50x - 2x^2, where x is the number of items sold. Find the total revenue generated when 10 items are sold.

• 400

• 250

• 300

• 150

A rectangular garden has a length that varies with time according to the function L(t) = 2t + 5. If the width is constant at 3 meters, find the area of the garden after 4 hours.

• 45 square meters

• 30 square meters

• 39 square meters

• 25 square meters

A river's flow rate is modeled by the function f(t) = 3t^2 + 2t. Calculate the total flow of water from the river over a 3-hour period.

• 48

• 18

• 36

• 24

A student studies for a test, and the effectiveness of their study time can be modeled by the function E(t) = 10t - t^2, where t is in hours. Find the average effectiveness of their study time from 0 to 4 hours.

• 10.5

• 12.33

• 14.67

• 20