Analyzing Costs: Slope and Intercept in Real-World Problems

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. If the total cost is represented by the equation C = 50 + 0.2m, where C is the cost and m is the miles driven, what is the slope of the line?

• 0.10

• 0.2

• 1.0

• 0.5

A scientist is studying the growth of bacteria, which doubles every hour. If the number of bacteria after t hours is represented by the equation N = N0 * 2^t, where N0 is the initial number, how does the graph of this equation behave?

• The graph exhibits exponential growth, increasing steeply over time.

• The graph oscillates between increasing and decreasing.

• The graph decreases steadily over time.

• The graph remains constant over time.

A phone company offers a plan that costs $30 per month plus $0.10 per text message. Write the equation for the total cost C in terms of the number of text messages m. What is the y-intercept of this equation?

• $10

• 30

• $0

• $50

A store sells a product for $20, and the price decreases by $2 for every 10 units sold. Write the equation for the price P in terms of the number of units sold x. What does the slope represent in this context?

• P = 20 - 0.2x; the slope represents the decrease in price per unit sold.

• P = 20 + 0.2x; the slope represents the increase in price per unit sold.

• P = 20 - 2x; the slope represents the total price decrease after selling units.

• P = 18 - 0.5x; the slope represents the total price after selling units.

A population of fish in a lake is modeled by the equation P = 1000/(1 + 9e^(-0.1t)), where P is the population and t is time in years. What does the slope of the tangent line at t = 5 indicate about the population growth?

• The slope of the tangent line at t = 5 indicates the rate of population growth at that time.

• The slope of the tangent line at t = 5 represents the average population over the last 5 years.

• The slope of the tangent line at t = 5 indicates the maximum population capacity of the lake.

• The slope of the tangent line at t = 5 shows the total population at that time.

A gym charges a membership fee of $40 plus $5 for each class attended. If the total cost is represented by the equation C = 40 + 5c, where C is the cost and c is the number of classes, what is the slope and what does it represent?

• The slope is 5, representing the cost per class attended.

• The slope is 10, representing the cost of two classes attended.

• The slope is 5, representing the total cost of all classes.

• The slope is 40, representing the total membership fee.

A delivery service charges a base fee of $15 plus $0.50 per mile. If the total cost is represented by the equation C = 15 + 0.5d, where d is the distance in miles, what is the y-intercept and what does it signify?

• $0

• $30

• $10

• 15

A researcher finds that the time it takes for a chemical reaction to complete can be modeled by the equation T = 200 - 10log(x), where x is the concentration of the reactant. What does the slope of this equation tell us about the relationship between concentration and time?

• The slope of -10 indicates no relationship between concentration and time.

• The slope of -10 means that higher concentrations lead to longer reaction times.

• The slope of -10 shows that time increases as concentration increases.

• The slope of -10 indicates that as concentration increases, the time for the reaction to complete decreases.

A subscription box service charges $25 per month plus $3 for each item included. Write the equation for the total cost C in terms of the number of items n. What does the slope represent in this scenario?

• C = 25 + 3n; the slope represents the cost per item.

• C = 25n + 3; the slope represents the total cost.

• C = 3n; the slope represents the number of items.

• C = 3 + 25n; the slope represents the monthly fee.

A local bakery sells cupcakes for $3 each and offers a discount of $1 for every 5 cupcakes purchased. Write the equation for the total cost C in terms of the number of cupcakes x. What is the slope of this equation and what does it indicate about the pricing structure?

• C = 2x + 5

• C = 5x - 1

• C = (14/5)x

• C = 3x