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WorksheetsUnderstanding Slopes and Graphs: Linear vs. Exponential
Total questions: 8
Worksheet time: 4mins
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.
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
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.
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.
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.
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
