Evaluating and Graphing Exponential Functions in Depth

A population of bacteria doubles every 3 hours. If there are initially 500 bacteria, how many will there be after 12 hours? Evaluate the exponential function to find the answer.

• 4000

• 10000

• 8000

• 6000

The value of a car decreases by 15% each year. If the car is currently worth $20,000, what will its value be after 5 years? Use the exponential decay formula to evaluate.

• $8,874

• $15,000

• $12,000

• $10,500

A certain investment grows at an annual rate of 8%. If you invest $1,000, how much will it be worth after 10 years? Evaluate the exponential function to find the future value.

• 1800.50

• 2158.92

• 1500.00

• 2000.00

A tree grows at a rate of 5% per year. If the tree is currently 10 feet tall, how tall will it be after 4 years? Use the exponential growth formula to evaluate the height.

• 10 feet

• 15 feet

• 12.16 feet

• 8 feet

The half-life of a radioactive substance is 10 years. If you start with 80 grams, how much will remain after 30 years? Evaluate the exponential decay function to find the remaining amount.

• 10 grams

• 20 grams

• 5 grams

• 40 grams

Graph the function f(x) = 2^x. Identify the key features of the graph, including the y-intercept and the behavior as x approaches negative and positive infinity.

• Key features: y-intercept at (0, 1); as x -> -∞, f(x) -> 0; as x -> +∞, f(x) -> ∞.

• y-intercept at (0, 0); as x -> -∞, f(x) -> -∞; as x -> +∞, f(x) -> 0.

• y-intercept at (1, 0); as x -> -∞, f(x) -> 1; as x -> +∞, f(x) -> 1.

• y-intercept at (0, 2); as x -> -∞, f(x) -> 2; as x -> +∞, f(x) -> ∞.

A certain species of fish in a lake grows exponentially. If the population is modeled by the function P(t) = 200e^(0.3t), where t is time in years, how many fish will there be after 5 years? Evaluate the function to find the population.

• 1200

• 896

• 750

• 500

The number of users of a new app is modeled by the function U(t) = 150(1.5)^t, where t is the number of months since launch. How many users will there be after 6 months? Evaluate the exponential function to find the answer.

• 1709

• 900

• 1200

• 2500

A bank offers a savings account with a 6% interest rate compounded annually. If you deposit $2,000, how much will you have after 8 years? Use the exponential growth formula to evaluate the total amount.

• 2800.50

• 2500.00

• 4000.00

• 3187.70

Graph the function g(x) = 3(0.5)^x. Describe the characteristics of the graph, including the y-intercept and the asymptotic behavior as x increases.

• The y-intercept is (0, 3) and the graph approaches y = 0 as x increases.

• The y-intercept is (0, 1) and the graph approaches y = -1 as x increases.

• The y-intercept is (0, 3) and the graph approaches y = 10 as x increases.

• The y-intercept is (0, 0) and the graph approaches y = 5 as x increases.