Decoding Exponential Decay: Word Problems & Models

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

• 40 grams

• 10 grams

• 20 grams

A car's value decreases by 20% each year. If the car is currently worth $15,000, what will its value be after 3 years?

• $5,000

• $7,680

• $10,000

• $12,000

A population of bacteria decreases from 1,000 to 250 in 6 hours. What is the decay rate per hour?

• 0.500

• 0.300

• 0.1542

• 0.075

A certain type of medicine loses its effectiveness at a rate of 10% per hour. If a patient takes a dose of 200 mg, how much will be effective after 3 hours?

• 145.8 mg

• 200 mg

• 180 mg

• 120 mg

A tree's height decreases by 5% each year due to disease. If the tree is currently 10 meters tall, what will its height be after 4 years?

• 7.5 meters

• 6.3 meters

• 8.1450625 meters

• 9 meters

A car depreciates in value according to the model V(t) = 20000(0.85)^t, where t is the number of years. What will the value be after 5 years?

• 10000.00

• 7500.50

• 8874.00

• 12000.00

A certain species of fish decreases in population by 15% each year. If the initial population is 500, what will the population be after 4 years?

• 350

• 261

• 200

• 400

A certain chemical compound decays exponentially. If 100 grams remain after 10 hours, how much was present initially if the decay constant is 0.1?

• 200 grams

• 150 grams

• 300 grams

• 271.83 grams

A smartphone loses 30% of its value each year. If it was purchased for $800, what will its value be after 2 years?

• 560

• 392

• 480

• 640

A forest area decreases by 12% annually due to logging. If the initial area is 1,000 hectares, what will the area be after 3 years?

• 900 hectares

• 681.47 hectares

• 750 hectares

• 800 hectares