Growth and Decay: Real-World Applications of Base e

A population of bacteria grows continuously at a rate of 5% per hour. If the initial population is 200, how many bacteria will there be after 3 hours? Use the formula P = Pe^(rt).

• 232

• 300

• 150

• 250

A certain radioactive substance decays at a rate of 3% per year. If you start with 500 grams, how much of the substance will remain after 5 years?

• 429.37 grams

• 400 grams

• 500 grams

• 450 grams

A bank offers an investment that grows continuously at an annual interest rate of 4%. If you invest $1,000, how much will you have after 10 years?

• 1800.50

• 2000.00

• 1491.82

• 1200.00

A car's value decreases continuously at a rate of 15% per year. If the car was purchased for $20,000, what will its value be after 4 years?

• $15,000.00

• $12,500.00

• $10,448.13

• $8,000.00

A certain species of fish in a lake is observed to grow at a rate of 8% per month. If there are initially 150 fish, how many will there be after 6 months?

• 180

• 210

• 300

• 238

A certain medication in the bloodstream decreases at a rate of 10% per hour. If the initial concentration is 80 mg, what will the concentration be after 3 hours?

• 70 mg

• 65 mg

• 58.32 mg

• 45 mg

A tree's height increases continuously at a rate of 6% per year. If the tree is currently 10 feet tall, how tall will it be after 5 years?

• 15.00 feet

• 12.00 feet

• 13.38 feet

• 10.50 feet

A population of rabbits doubles every 4 months. If there are currently 50 rabbits, how many will there be after 1 year?

• 150

• 300

• 400

• 200

A certain investment grows continuously at a rate of 7% per year. If you invest $2,500, how much will you have after 5 years?

• $2,500.00

• $4,000.00

• $3,000.00

• $3,547.67

A certain type of mold grows at a rate of 12% per day. If you start with 10 grams, how much will you have after 3 days?

• 15 grams

• 12 grams

• 10 grams

• 14.05 grams