Modeling Real-Life Exponential Growth and Decay

A population of bacteria grows continuously at a rate of 5% per hour. If the initial population is 100, how many bacteria will there be after 3 hours? Use the formula N = N0 * e^(rt).

• 116

• 150

• 90

• 200

A certain radioactive substance decays at a rate of 3% per year. If you start with 50 grams, how much of the substance will remain after 5 years?

• 42.94 grams

• 45 grams

• 50 grams

• 40 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?

• 1600.00

• 1800.50

• 1491.82

• 1200.00

A certain species of fish in a lake is observed to grow at a continuous rate of 6% per month. If there are currently 200 fish, how many will there be after 4 months?

• 200

• 150

• 254

• 300

A car's value decreases continuously at a rate of 15% per year. If the car was originally worth $20,000, what will its value be after 2 years?

• $16,000

• $12,000

• $14,450

• $18,000

A certain type of mold grows at a continuous rate of 8% per day. If you start with 10 grams of mold, how much will you have after 7 days?

• 15 grams

• 17.49 grams

• 20 grams

• 12.5 grams

A tree's height increases continuously at a rate of 10% per year. If the tree is currently 5 meters tall, how tall will it be after 3 years?

• 6.655 meters

• 8.1 meters

• 7.2 meters

• 5.5 meters

A certain investment doubles in value every 5 years due to continuous compounding. If you invest $500, how much will it be worth after 15 years?

• 2500

• 1500

• 3000

• 4000

A population of rabbits is modeled by the equation P(t) = P0 * e^(kt), where P0 is the initial population and k is the growth rate. If the initial population is 50 and k is 0.1, what will the population be after 10 years?

• 136

• 200

• 90

• 75

A certain chemical reaction occurs at a rate of 12% per hour. If you start with 80 grams of the reactant, how much will remain after 4 hours?

• 75 grams

• 47.98 grams

• 32 grams

• 60 grams