Precalculus: Graphing & Solving Word Problems Challenge

A car's distance from a starting point is modeled by the function d(t) = 5t + 10, where d is in miles and t is in hours. Graph this function and determine the distance after 3 hours.

• 25 miles

• 20 miles

• 30 miles

• 15 miles

The height of a ball thrown into the air is modeled by the equation h(t) = -16t^2 + 32t + 5, where h is the height in feet and t is the time in seconds. Solve for the time when the ball hits the ground.

• 4.0 seconds

• 3.0 seconds

• 1.5 seconds

• 2.5 seconds

A company's profit P(x) is given by the function P(x) = -2x^2 + 12x - 8, where x is the number of units sold. Graph this function and find the maximum profit.

• 8

• 10

• 12

• 5

The temperature T in degrees Celsius of a substance over time is modeled by T(t) = 20 + 10e^(-0.5t). Solve for t when T(t) reaches 25 degrees Celsius.

• 2.5000

• 1.3863

• 1.0000

• 3.1415

A rectangular garden's area A is given by the function A(x) = x(10 - x), where x is the width in meters. Graph this function and find the width that maximizes the area.

• 5 meters

• 3 meters

• 7 meters

• 10 meters

The revenue R from selling x items is modeled by R(x) = 50x - 0.5x^2. Solve for x when the revenue is $1000 and graph the revenue function.

• x ≈ 71.07 or x ≈ 28.93

• x ≈ 100.00

• x ≈ 50.00

• x ≈ 10.00

A population of bacteria grows according to the function P(t) = 100e^(0.3t). Graph this function and determine the population after 5 hours.

• 500

• 600

• 300

• 448

The cost C of producing x items is given by C(x) = 3x + 200. Solve for x when the cost is $500 and graph the cost function.

• 250

• 150

• 200

• 100

A projectile's height is modeled by the equation h(t) = -4.9t^2 + 20t + 1. Solve for the time when the projectile reaches its maximum height and graph the height function.

• 2.75 seconds

• 1.50 seconds

• 3.00 seconds

• 2.04 seconds

The profit function P(x) = -x^2 + 40x - 300 represents a business's profit based on the number of items sold. Graph this function and find the number of items that maximizes profit.

• 20

• 30

• 25

• 15