Mastering Exponential Equations and Growth Patterns

A bacteria culture doubles in size every 3 hours. If the initial population is 500, write an exponential equation to represent the population after t hours. What will the population be after 12 hours?

• 10000

• 4000

• 6000

• 8000

A car's value decreases by 15% each year. If the car is currently worth $20,000, write an exponential equation to model its value over time. How much will the car be worth after 5 years?

• $12,000 after 5 years

• The car will be worth approximately $8,874 after 5 years.

• $15,000 after 5 years

• $10,500 after 5 years

A tree grows at a rate of 10% per year. If the tree is currently 2 meters tall, write an exponential equation to represent its height after t years. How tall will the tree be after 4 years?

• 3.5 meters

• 2.5 meters

• 2.93 meters

• 4.1 meters

A certain investment grows at an annual rate of 8%. If you invest $1,000, write an exponential equation to model the investment's value over time. What will the value be after 10 years?

• 2158.92

• 2500.00

• 1800.50

• 2000.00

A population of fish in a lake is currently 1,000 and is expected to grow by 25% each year. Write an exponential equation to represent the fish population after t years. How many fish will there be after 3 years?

• 1200

• 2500

• 1953

• 1500

A smartphone's battery life decreases exponentially. If it starts with a full charge of 100%, and loses 20% of its charge every hour, write an exponential equation to represent the battery life after t hours. What will the battery percentage be after 5 hours?

• 75%

• 32.77%

• 50%

• 10%

A viral video on a social media platform gains 1,000 views in the first hour and then doubles its views every hour. Write an exponential equation to represent the number of views after t hours. How many views will the video have after 4 hours?

• 20000

• 4000

• 8000

• 16000

A savings account earns 5% interest compounded annually. If you deposit $500, write an exponential equation to model the amount in the account after t years. How much will be in the account after 6 years?

• $500.00

• $800.00

• $600.00

• $676.84

A certain species of plant grows exponentially. If the initial number of plants is 50 and it doubles every month, write an exponential equation to represent the number of plants after t months. How many plants will there be after 6 months?

• 1600

• 4000

• 3200

• 800

A town's population is currently 10,000 and is expected to grow by 3% each year. Write an exponential equation to model the population growth. What will the population be in 5 years?

• 10500

• 12000

• 11000

• 11592.74