Linear vs. Exponential: Functions and Their Graphs

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. Write the linear function that represents the total cost (C) in terms of miles driven (m).

• C(m) = 50 - 0.20m

• C(m) = 50 + 0.50m

• C(m) = 0.20m

• C(m) = 50 + 0.20m

A bacteria culture doubles in size every hour. If the initial size is 100 bacteria, write an exponential function that represents the size of the culture after t hours.

• f(t) = 100 * 2^t

• f(t) = 100 + 2^t

• f(t) = 100 * 3^t

• f(t) = 50 * 2^t

A local gym has a membership fee of $30 per month. If they have 50 members, write a linear function to represent the total monthly income (I) from memberships.

• I = 50m

• I = 30 + m

• I = 30m, where m is the number of members.

• I = 15m

A tree grows at a rate of 5% per year. If the tree is currently 10 feet tall, write an exponential function to represent its height (H) after t years.

• H(t) = 10 * (0.95)^t

• H(t) = 10 + 5t

• H(t) = 10 * (1.05)^t

• H(t) = 10 * (1.10)^t

A phone company offers a plan that costs $40 per month plus $0.10 per text message. Write the linear function for the total cost (C) based on the number of text messages (n) sent.

• C(n) = 40 + 0.10n

• C(n) = 0.10n - 40

• C(n) = 40 + n

• C(n) = 40n + 0.10

A population of rabbits increases by 15% each year. If there are currently 200 rabbits, write an exponential function to model the population after t years.

• P(t) = 200 + 15t

• P(t) = 200 * (1.05)^t

• P(t) = 200 * (1.15)^t

• P(t) = 200 * (0.85)^t

A taxi service charges a base fare of $3 plus $2 per mile. Write the linear equation that represents the total fare (F) based on the number of miles (m) driven.

• F = 2m - 3

• F = 3m + 2

• F = 2 + 3m

• F = 3 + 2m

A savings account earns 4% interest compounded annually. If you start with $1,000, write an exponential function to represent the amount of money (A) in the account after t years.

• A(t) = 1000 + 1000(0.04)^t

• A(t) = 1000(0.04)^t

• A(t) = 1000(1.04)^t

• A(t) = 1000(1.04)t

A factory produces 500 units of a product each day. If production increases by 10 units each day, write a linear function to represent the total production (P) after d days.

• P(d) = 500d

• P(d) = 490 + 5d

• P(d) = 490 + 10d

• P(d) = 500 + 10d

A viral video gets 1,000 views on the first day and doubles its views each subsequent day. Write an exponential function to represent the total views (V) after d days.

• V(d) = 1000 * 2^d

• V(d) = 1000 + 2^d

• V(d) = 1000 * d

• V(d) = 1000 * 3^d