Analyzing Real-Life Functions and Their Parameters

A ball is thrown upwards from a height of 2 meters. The height of the ball in meters after t seconds is given by the equation h(t) = -5t^2 + 10t + 2. Analyze the function behavior to determine the maximum height the ball reaches.

• 3 meters

• 10 meters

• 5 meters

• 7 meters

A taxi company charges a flat fee of $3 plus $2 per mile driven. Write a linear function to represent the total cost C in dollars for driving m miles. Interpret the slope of the function in the context of the problem.

• C(m) = 2m

• C(m) = 3m + 2

• C(m) = 3 + 2m

• C(m) = 3 + m

Tags

CCSS.HSF.LE.B.5

The population of a small town is modeled by the function P(t) = 500e^(0.03t), where t is the number of years since 2020. Analyze the function to determine the population after 5 years and interpret the growth rate.

• 600

• 550

• 581

• 500

A rectangular garden has a length that is 3 meters longer than its width. If the area of the garden is 40 square meters, write a quadratic equation to represent the relationship between the width w and the area. Solve for the width and interpret the results.

• The width of the garden is 4 meters.

• The width of the garden is 7 meters.

• The width of the garden is 6 meters.

• The width of the garden is 5 meters.

The cost of producing x items is given by the function C(x) = 50 + 10x. If the company sells the items for $20 each, write a linear function for revenue R(x) and determine the break-even point by setting C(x) equal to R(x).

• 5

• 10

• 7

• 3

Tags

CCSS.8.EE.C.8C

A car's value decreases exponentially over time. If the initial value of the car is $20,000 and it loses 15% of its value each year, write an exponential decay function to model its value after t years. Analyze the function to find the car's value after 3 years.

• $8,500

• $12,282.50

• $10,000

• $15,000

A farmer wants to fence a rectangular field with a perimeter of 100 meters. Write a quadratic function for the area A of the field in terms of its width w. Analyze the function to find the dimensions that maximize the area.

• Width = 25 meters, Length = 25 meters.

• Width = 10 meters, Length = 40 meters.

• Width = 15 meters, Length = 35 meters.

• Width = 20 meters, Length = 30 meters.

The temperature in a city can be modeled by the function T(t) = 30 + 10sin(πt/12), where t is the time in hours. Interpret the parameters of the function to explain the temperature variation throughout the day.

• The temperature remains constant at 30 degrees throughout the day.

• The average temperature is 25 degrees with a variation of ±5 degrees.

• The average temperature is 30 degrees, with a variation of ±10 degrees throughout the day.

• The temperature fluctuates between 20 and 40 degrees.

A company's profit P can be modeled by the quadratic function P(x) = -2x^2 + 12x - 10, where x is the number of units sold. Analyze the function to find the number of units that maximizes profit and interpret the significance of this value.

• 2

• 4

• 5

• 3

The height of a plant is modeled by the exponential function H(t) = 5(1.2^t), where t is the number of weeks since planting. Analyze the function to determine how tall the plant will be after 4 weeks and interpret the growth factor.

• 15.000

• 10.368

• 12.432

• 8.256