Mastering Exponential Decay and Half-Life Calculations

A radioactive substance has a half-life of 5 years. If you start with 80 grams, how much will remain after 15 years?

• 5 grams

• 20 grams

• 40 grams

• 10 grams

A certain bacteria culture doubles every 3 hours. If you start with 500 bacteria, how many will there be after 12 hours?

• 8000

• 4000

• 16000

• 1000

A car's value decreases by 20% each year. If the car is initially worth $25,000, what will its value be after 3 years?

• $12,800

• $15,000

• $10,000

• $20,000

A certain medication in the bloodstream decreases by 25% every hour. If the initial amount is 200 mg, how much will be left after 4 hours?

• 50 mg

• 63.28 mg

• 150 mg

• 100 mg

A tree loses 10% of its leaves each autumn. If it starts with 1,000 leaves, how many leaves will it have left after 2 autumns?

• 1000

• 750

• 900

• 810

A certain type of fish population decreases by 15% each year. If the initial population is 1,200 fish, what will the population be after 2 years?

• 900

• 867

• 1,200

• 1,000

A radioactive isotope has a decay constant of 0.693 per year. If you have 100 grams, how much will remain after 1 year?

• 50 grams

• 100 grams

• 25 grams

• 75 grams

A car depreciates in value according to the model V(t) = 20000e^(-0.15t), where V is the value in dollars and t is the time in years. What will the value be after 5 years?

• 8000.00

• 15000.00

• 9448.00

• 12000.00

A certain type of mold grows at a rate of 30% per day. If you start with 50 grams, how much will there be after 2 days?

• 75 grams

• 60 grams

• 84.5 grams

• 100 grams

A certain chemical has a half-life of 10 minutes. If you start with 160 mg, how much will remain after 30 minutes?

• 20 mg

• 100 mg

• 80 mg

• 40 mg