Exponential Growth & Decay: Real-World Applications

A bacteria culture doubles in size every hour. If the culture starts with 5 bacteria, how many will there be after x hours?

• 5 * (2^x)

• 5 + (2^x)

• 10 * (2^x)

• 5 * x

A certain investment grows at a rate of 8% per year. If you invest $1,000, how much will it be worth after x years?

• 1000(1.08)^x

• 1000(1.10)^x

• 1000(1.05)^x

• 1000(1.08)x

A tree grows at a rate of 1.5 times its height each year. If the tree is currently 2 meters tall, how tall will it be after x years?

• 2 * (1.5^x)

• 2 * (x^1.5)

• 2 + (1.5 * x)

• 1.5 * (2 + x)

A population of rabbits increases by a factor of 3 every year. If there are currently 10 rabbits, how many will there be after x years?

• 10 * (2^x)

• 10 * (3^x)

• 10 * x

• 10 + (3^x)

A car's value decreases to half its value every 5 years. If the car is currently worth $20,000, what will its value be after x periods of 5 years?

• 20000 / (2^x)

• 20000 * (1/2)^x

• 20000 - 5000 * x

• 20000 * (1/3)^x

A viral video gets 4 times more views each day. If it starts with 200 views, how many views will it have after x days?

• 200 * (2^x)

• 400 * (4^x)

• 200 + (4^x)

• 200 * (4^x)

A savings account earns interest that compounds annually. If you start with $500 and it doubles every 6 years, how much will you have after x periods of 6 years?

• 500 * (2^x)

• 500 * (3^x)

• 1000 * (2^x)

• 500 + (100 * x)

A certain species of fish triples in population every year. If there are currently 15 fish, how many will there be after x years?

• 15 * 3^x

• 15 - 3^x

• 15 + 3^x

• 15 * 2^x

A smartphone's battery life decreases to 75% of its original capacity every year. If the battery lasts 24 hours initially, how long will it last after x years?

• 24 * (1.25^x) hours

• 24 * (0.75^x) hours

• 24 + (0.75 * x) hours

• 24 - (0.25^x) hours

A certain type of mold grows at a rate of 2 times its size every 3 days. If it starts at 10 grams, how much will it weigh after x periods of 3 days?

• 10 + (2^x)

• 10 * (2^x)

• 10 * (2+x)

• 10 * (3^x)