Understanding Slopes and Graphs: Linear vs. Exponential

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. Write the equation for the total cost (C) in terms of miles driven (m). What is the slope and what does it represent?

• C = 50 + 0.20m; slope = 0.20, representing the cost per mile.

• C = 50m; slope = 50, representing the flat fee.

• C = 0.20 + 50m; slope = 50, representing the cost per mile.

• C = 50 + 0.50m; slope = 0.50, representing the total cost.

Tags

CCSS.HSF.LE.B.5

A population of bacteria doubles every 3 hours. If there are initially 100 bacteria, write an exponential function to represent the population after t hours. How many bacteria will there be after 9 hours?

• 600

• 1000

• 400

• 800

Tags

CCSS.HSF.LE.A.2

A city’s population is modeled by the equation P(t) = 5000(1.05)^t, where t is the number of years since 2020. What is the initial population, and what does the base of the exponent represent?

• The initial population is 5000, and the base of the exponent (1.05) represents a 5% annual growth rate.

• The initial population is 5000, and the base of the exponent (1.05) represents a 2% annual growth rate.

• The initial population is 6000, and the base of the exponent (1.05) represents a 10% annual growth rate.

• The initial population is 4000, and the base of the exponent (1.05) represents a 5% annual decline rate.

Tags

CCSS.HSF.LE.B.5

A gardener plants a tree that grows 2 inches per month. Write a linear equation to represent the height (h) of the tree after m months. What is the y-intercept and what does it signify?

• h = m; y-intercept = 2

• h = 2m + 5; y-intercept = 5

• h = 2m; y-intercept = 0

• h = 3m; y-intercept = 1

A bank account earns interest according to the formula A = P(1 + r)^t, where A is the amount, P is the principal, r is the interest rate, and t is time in years. If you invest $1000 at an interest rate of 5% for 3 years, how much will you have?

• 1200.00

• 1157.63

• 1100.50

• 1050.00

A linear equation representing the cost of a gym membership is C = 30 + 10m, where m is the number of months. What is the fixed cost and what does it represent? How much would it cost for 6 months?

• The fixed cost is 10, and the total cost for 6 months is 60.

• The fixed cost is 30, and the total cost for 6 months is 90.

• The fixed cost is 50, and the total cost for 6 months is 150.

• The fixed cost is 30, and the total cost for 6 months is 120.

Tags

CCSS.HSF.LE.B.5

A phone company offers a plan that costs $40 per month plus $0.10 per text message. Write the equation for the total cost (C) in terms of the number of text messages (n). What does the slope represent?

• C = 40 + 0.10n; the slope represents the cost per text message.

• C = 40n + 0.10; the slope represents the total monthly cost.

• C = 40 + 0.05n; the slope represents the discount per text message.

• C = 0.10 + 40n; the slope represents the fixed cost.

Tags

CCSS.HSF.LE.B.5

A linear function describes the distance (d) a train travels over time (t) as d = 60t. If the train travels for 2.5 hours, how far does it go? What does the slope indicate about the train's speed?

• 200 miles

• 120 miles

• 150 miles

• 180 miles

Tags

CCSS.HSF.LE.B.5