Analyzing Exponential Growth: Domains and Graphs

A population of bacteria doubles every 3 hours. If the initial population is 500, what is the domain of the function that models this growth?

• (0, 1000]

• [0, ∞)

• [500, 1000]

• [-3, 3]

A car's value decreases exponentially over time. If the car is worth $20,000 now and loses 15% of its value each year, what is the domain of the function that represents its value over time?

• (-∞, 0)

• [0, ∞)

• [0, 20,000]

• (0, 20,000]

A bank offers an account that compounds interest exponentially. If you deposit $1,000 at an annual interest rate of 5%, what is the domain of the function that models your account balance over time?

• [1,000, ∞)

• (-∞, 0)

• (0, 1,000)

• [0, ∞)

A certain species of fish in a lake grows exponentially. If the population is currently 1,000 and grows by 20% each year, how would you graph this function?

• P(t) = 1000 + 200t

• P(t) = 1000 * (1.1)^t

• P(t) = 1000 * (0.8)^t

• The function can be graphed as P(t) = 1000 * (1.2)^t.

A tree grows exponentially, reaching a height of 10 feet in 5 years. If the growth can be modeled by an exponential function, what is the domain of this function?

• (-∞, 10]

• (0, 5)

• [5, 10]

• [0, ∞)

A virus spreads exponentially in a closed environment. If it starts with 10 infected individuals and doubles every day, what is the domain of the function that models the number of infected individuals?

• {1, 2, 3, ...}

• {0, 0.5, 1, ...}

• {10, 20, 30, ...}

• {0, 1, 2, ...}

A company’s revenue grows exponentially. If the revenue is currently $50,000 and increases by 25% each year, how would you graph this function and determine its domain?

• The domain is t >= 0, and the function can be graphed as R(t) = 50000 * (1.25)^t.

• The domain is t >= 0, and the function can be graphed as R(t) = 50000 + 0.25t.

• The domain is t < 0, and the function is R(t) = 50000 * (0.75)^t.

• The domain is t >= 1, and the function can be graphed as R(t) = 50000 * (1.5)^t.

A certain type of investment grows exponentially. If you invest $2,000 and it grows to $8,000 in 4 years, what is the domain of the function that models this investment?

• [0, 2]

• [0, 8]

• [2, 4]

• [0, 4]

A city’s population is projected to grow exponentially. If the current population is 150,000 and it is expected to double every 10 years, what is the domain of the function that models this growth?

• t >= 0, t is a multiple of 5

• t is any integer

• t >= 0, t is a multiple of 10

• t < 0

A radioactive substance decays exponentially. If you start with 80 grams and it decays to half its amount every 5 years, how would you graph this function and determine its domain?

• The domain is [0, ∞) and the function is A(t) = 80 * (1/2)^(t/5).

• The domain is [0, 10] and the function is A(t) = 80 * (1/3)^(t/5).

• The domain is (-∞, 0) and the function is A(t) = 80 * e^(-t/5).

• The domain is [0, ∞) and the function is A(t) = 80 * (1/4)^(t/5).