Exploring Real-Life Functions: Graphing & Word Problems

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. Write a linear equation to represent the total cost (C) in terms of miles driven (m). Graph this equation and interpret the slope.

• C = 50 - 0.20m

• C = 50 + 0.20m

• C = 50 + 0.50m

• C = 0.20 + 50m

A ball is thrown upwards from a height of 2 meters with an initial velocity of 10 m/s. The height (h) of the ball after t seconds can be modeled by the equation h(t) = -4.9t^2 + 10t + 2. Graph this quadratic function and determine the maximum height of the ball.

• 7.04 meters

• 10 meters

• 3.2 meters

• 5.5 meters

A population of bacteria doubles every 3 hours. If the initial population is 100, write an exponential function to model the population (P) after t hours. Graph this function and interpret the growth rate.

• P(t) = 100 + 2t

• P(t) = 100 * 2^(t/3)

• P(t) = 100 * 3^(t/3)

• P(t) = 100 * 2^(t/6)

A store sells a new smartphone for $800. Each month, the price decreases by $50. Write a linear equation to represent the price (P) after m months. Graph this equation and find the month when the price will be $300.

• 10 months

• 5 months

• 12 months

• 8 months

A farmer plants a tree that grows according to the function h(t) = 5t^2 + 2, where h is the height in meters and t is the time in years. Graph this quadratic function and interpret the growth pattern of the tree over time.

• The tree's height decreases linearly over time.

• The tree's height increases exponentially over time.

• The tree's height remains constant over time.

• The tree's height increases quadratically over time, indicating accelerated growth.

A city’s population is modeled by the function P(t) = 5000(1.03)^t, where t is the number of years since 2020. Graph this exponential function and interpret what the growth factor represents.

• The growth factor of 1.03 represents a 3% decrease in the city's population.

• The growth factor of 1.03 indicates a 1% annual decrease in the city's population.

• The growth factor of 1.03 represents a 3% annual increase in the city's population.

• The growth factor of 1.03 means the population will double every 10 years.

A rocket is launched from the ground with an initial velocity of 30 m/s. The height (h) of the rocket after t seconds can be modeled by the equation h(t) = -5t^2 + 30t. Graph this quadratic function and find the time when the rocket reaches its maximum height.

• 2 seconds

• 4 seconds

• 5 seconds

• 3 seconds

A subscription service charges $10 per month plus a one-time setup fee of $25. Write a linear equation to represent the total cost (C) after m months. Graph this equation and interpret the y-intercept.

• C = 15m + 25

• C = 25m + 10

• C = 10m - 25

• C = 10m + 25

A savings account earns interest at a rate of 5% compounded annually. If you start with $1000, write an exponential function to model the amount (A) after t years. Graph this function and interpret the significance of the initial amount.

• A(t) = 1000(0.05)^t

• A(t) = 1000(1.10)^t

• A(t) = 1000(1.05)^t

• A(t) = 1000(1.05)^t + 1000

A local gym has a membership fee of $40 plus $5 per class attended. Write a linear equation to represent the total cost (C) in terms of classes attended (c). Graph this equation and determine the cost for attending 10 classes.

• $70

• $100

• $50

• $90