Mastering Exponential Equations and Graphs in Real Life

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

• 8000

• 6000

• 10000

• 4000

The value of a car decreases exponentially over time. If a car is worth $20,000 and loses 15% of its value each year, what will its value be after 5 years? Use an exponential decay model to solve.

• $12,000.00

• $15,500.00

• $8,874.00

• $10,200.00

A certain investment grows exponentially at a rate of 8% per year. If you invest $1,000, how much will it be worth after 10 years? Solve the exponential equation to find the future value.

• 2000.75

• 2158.92

• 1800.50

• 1500.00

The half-life of a radioactive substance is 5 years. If you start with 80 grams, how much will remain after 15 years? Set up and solve the exponential decay equation.

• 20 grams

• 10 grams

• 40 grams

• 5 grams

A bank offers an account that compounds interest annually at a rate of 5%. If you deposit $1,200, how much will you have in the account after 3 years? Graph the exponential growth function to visualize the growth.

• $1,389.15

• $1,800.00

• $1,500.00

• $1,200.00

A tree grows at a rate of 10% per year. If the tree is currently 2 meters tall, how tall will it be after 4 years? Solve the exponential growth equation to find the height.

• 4.00 meters

• 2.93 meters

• 2.00 meters

• 3.50 meters

The population of a city is modeled by the function P(t) = 50,000e^(0.03t), where t is the number of years since 2020. What will the population be in 2025? Use the exponential function to calculate the population.

• 50000

• 60000

• 58090

• 55000

A certain type of bacteria grows according to the function N(t) = 200e^(0.5t). How many bacteria will there be after 4 hours? Solve the exponential equation to find N(4).

• 2000

• 1478

• 1200

• 800

A loan of $5,000 is taken out with an interest rate of 6% compounded annually. How much will be owed after 3 years? Use the exponential growth formula to find the total amount owed.

• $4,800.00

• $6,200.00

• 5955.08

• $5,500.00

The formula for the amount of a substance remaining after t years is A(t) = A_0(1/2)^(t/h), where A_0 is the initial amount and h is the half-life. If the half-life is 10 years and you start with 100 grams, how much will remain after 30 years? Solve the equation to find the remaining amount.

• 50 grams

• 5 grams

• 25 grams

• 12.5 grams