10th Grade: Graphing Growth & Decay Through Equations

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

• 8000

• 4000

• 10000

• 2000

A car's value decreases by 15% each year. If the car is currently worth $20,000, what will its value be after 5 years? Solve the differential equation to find the value over time.

• $10,500.00

• $15,000.00

• $8,874.34

• $12,000.00

A radioactive substance has a half-life of 10 years. If you start with 80 grams, how much will remain after 30 years? Use the exponential decay formula to solve.

• 40 grams

• 10 grams

• 20 grams

• 5 grams

The number of users of a new app increases by 20% each month. If there are 1,000 users at launch, how many users will there be after 6 months? Graph the growth function to visualize the increase.

• 1500

• 2500

• 3500

• 2986

A certain species of fish decreases in population by 10% each year due to overfishing. If the current population is 5,000, what will it be in 4 years? Solve the differential equation to find the future population.

• 4500

• 2500

• 4000

• 3281

A certain medication in the bloodstream decreases by 25% every hour. If the initial amount is 200 mg, how much will remain after 3 hours? Use the decay formula to find the remaining amount.

• 100 mg

• 150 mg

• 50 mg

• 84.375 mg

A town's population is 10,000 and is growing at a rate of 4% per year. What will the population be in 10 years? Graph the population growth function to illustrate the change.

• 12000

• 13500

• 14802

• 16000

A car depreciates continuously at a rate of 12% per year. If the car's initial value is $30,000, what will its value be after 3 years? Solve the differential equation to determine the car's value over time.

• 30000.00

• 18000.00

• 25000.00

• 20931.00