Exploring Exponential Growth: Real-Life Word Problems

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 and interpret the result.

• 8000

• 10000

• 2000

• 4000

A car's value 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? Set up and solve the exponential equation.

• $15,000.00

• $12,000.00

• $8,874.00

• $10,500.00

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? Write and solve the exponential equation to find the answer.

• 1500.00

• 2158.92

• 1800.50

• 2000.75

The half-life of a radioactive substance is 5 years. If you start with 80 grams, how much will remain after 15 years? Formulate and solve the exponential equation to determine the remaining amount.

• 5 grams

• 10 grams

• 20 grams

• 40 grams

A tree grows exponentially, increasing its height by 25% each year. If the tree is currently 2 meters tall, how tall will it be after 4 years? Create and solve the exponential equation to find the height.

• 4.88 meters

• 6.25 meters

• 5.00 meters

• 3.00 meters

A certain species of fish in a lake is known to triple in population every year. If there are currently 200 fish, how many will there be in 3 years? Solve the exponential equation to find the population after 3 years.

• 5400

• 600

• 1200

• 1800

A bank offers an account that compounds interest exponentially. If you deposit $500 at an interest rate of 5% compounded annually, how much will you have after 8 years? Set up and solve the exponential equation to find the total amount.

• 720.00

• 600.00

• 850.50

• 738.73

A smartphone's battery life decreases exponentially. If a fully charged battery lasts 24 hours, how long will it last after 3 cycles of use, assuming it retains 70% of its charge after each cycle? Solve the exponential equation to find the remaining battery life.

• 16 hours

• 12 hours

• 8.832 hours

• 20 hours

A certain type of mold grows exponentially. If it starts with 10 grams and doubles every 4 days, how much will there be after 16 days? Write and solve the exponential equation to determine the total amount of mold.

• 120 grams

• 200 grams

• 80 grams

• 160 grams

A city’s population is projected to grow exponentially. If the current population is 50,000 and it is expected to grow by 10% each year, what will the population be in 5 years? Formulate and solve the exponential equation to find the future population.

• 60000

• 75000

• 90000

• 80526