Exploring Exponential Growth: Graphs & Real-World Contexts

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

• 8000

• 10000

• 4000

• 2000

A car's value decreases by 20% each year. If the car is currently worth $15,000, what will its value be after 5 years? Write the equation and interpret the result in context.

• $7,500.00

• $10,000.00

• $3,000.00

• $4,915.20

A bank offers an interest rate of 5% compounded annually. If you deposit $1,000, how much will you have after 10 years? Solve the equation and graph the growth of your investment.

• $1,500.50

• $1,200.00

• $2,000.00

• $1,628.89

A tree grows at a rate of 1.5 times its height each year. If the tree is 2 feet tall now, how tall will it be after 4 years? Set up the equation and explain the growth in context.

• 8 feet

• 10.125 feet

• 12 feet

• 6.75 feet

A certain species of fish triples its population every year. If there are 200 fish now, how many will there be in 3 years? Solve the equation and discuss the implications of this growth.

• 1200

• 600

• 5400

• 1800

A smartphone's battery life decreases exponentially. If it lasts 24 hours when fully charged, how long will it last after 5 cycles of charging? Write the equation and interpret the result.

• The battery will last 12 hours after 5 cycles.

• The battery will last 48 hours after 5 cycles.

• The battery will last exactly 24 hours after 5 cycles.

• The battery will last significantly less than 24 hours after 5 cycles.

A certain type of investment grows exponentially. If you invest $2,000 and it doubles every 4 years, how much will you have after 16 years? Solve the equation and graph the growth.

• 32000

• 40000

• 24000

• 16000

A viral video gets 1,000 views on the first day and doubles its views each subsequent day. How many views will it have on the 7th day? Set up the equation and explain the significance of the result.

• 256000

• 64000

• 128000

• 32000

A savings account earns 3% interest compounded monthly. If you start with $500, how much will you have after 2 years? Write the equation and interpret the final amount in context.

• $530.85

• $520.00

• $510.25

• $540.50

A new technology is adopted by 10% of the population in the first year and increases by 50% each subsequent year. If the population is 1,000,000, how many will adopt it after 5 years? Solve the equation and discuss the growth trend.

• 1,318,750

• 1,000,000

• 2,000,000

• 500,000