Mastering Exponential Equations and Graphs in Real Life

1. A bacteria culture doubles in size every 3 hours. If the initial population is 500, write an exponential equation to represent the population after t hours. How many bacteria will there be after 12 hours?

• 4000

• 8000

• 16000

• 2000

2. The value of a car decreases exponentially over time. If a car is worth $20,000 and loses 15% of its value each year, write an exponential equation to model its value after t years. What will the car be worth after 5 years?

• $10,000.00

• $12,500.75

• $5,000.00

• $7,610.51

3. A certain investment grows exponentially at a rate of 8% per year. If you invest $1,000, write an equation to represent the amount of money after t years. How much will you have after 10 years?

• 1500.00

• 2000.00

• 2158.92

• 1800.50

4. The population of a small town is modeled by the equation P(t) = 2000e^(0.03t), where t is the number of years since 2000. What will the population be in 2025?

• 4234

• 5000

• 4000

• 3500

5. A radioactive substance decays exponentially. If the half-life of the substance is 5 years, and you start with 80 grams, how much will remain after 15 years?

• 40 grams

• 5 grams

• 20 grams

• 10 grams

6. A tree grows according to the model h(t) = 5(2^t), where h is the height in meters and t is the number of years. What will the height of the tree be after 4 years?

• 40 meters

• 60 meters

• 100 meters

• 80 meters

7. The number of views on a viral video increases exponentially. If it starts with 1,000 views and triples every week, write an equation to represent the views after t weeks. How many views will there be after 5 weeks?

• 10000

• 50000

• 729000

• 243000

8. A population of fish in a lake is modeled by the equation F(t) = 300(1.5^t). How many fish will there be after 4 years?

• 1519

• 2000

• 1800

• 1200

9. A loan of $5,000 is taken out with an interest rate of 6% compounded annually. Write an exponential equation to represent the amount owed after t years. How much will be owed after 3 years?

• $6,200.00

• $4,500.00

• $5,955.08

• $5,500.50

10. The height of a certain plant is modeled by the equation H(t) = 3(1.2^t), where H is the height in centimeters and t is the number of weeks. What will the height of the plant be after 6 weeks?

• 12.3 cm

• 10.5 cm

• 5.2 cm

• 8.96 cm