Mastering Exponential Functions: Growth & Decay Challenges

A population of bacteria doubles every 3 hours. If there are initially 500 bacteria, how many will there be after 12 hours? Graph the growth of the bacteria over this time period.

• 10000

• 2000

• 8000

• 4000

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? Solve the equation to find the value after 3 years and graph the depreciation.

• $7,680

• $12,000

• $10,000

• $5,000

A bank offers an account that compounds interest annually at a rate of 5%. If you deposit $1,000, how much will you have in the account after 5 years? Write and solve the exponential equation for this scenario.

• $1,200.00

• $1,276.28

• $1,500.00

• $1,000.00

The number of views on a viral video increases exponentially. If it starts with 1,000 views and triples every week, how many views will it have after 4 weeks? Graph the number of views over the 4 weeks.

• 27,000 views

• 50,000 views

• 81,000 views

• 10,000 views

A certain radioactive substance has a half-life of 10 years. If you start with 80 grams, how much will remain after 30 years? Solve the exponential decay equation and graph the remaining amount over time.

• 5 grams

• 20 grams

• 40 grams

• 10 grams

A tree grows at a rate of 10% per year. If the tree is currently 2 meters tall, what will its height be after 5 years? Write the exponential equation and solve it, then graph the height over the years.

• 2.5 meters

• 3.221 meters

• 4.0 meters

• 5.5 meters

A certain investment grows according to the function A(t) = 2000(1.07)^t, where A is the amount after t years. How much will the investment be worth after 10 years? Solve the equation and graph the growth.

• 3934.30

• 3000.75

• 4500.50

• 2500.00

A certain species of fish in a lake grows exponentially. If the initial population is 200 and it increases by 15% each year, how many fish will there be after 4 years? Write and solve the exponential equation, then graph the population over the years.

• 350

• 400

• 300

• 250

A smartphone's battery life decreases exponentially. If it starts at 100% and loses 25% of its charge every hour, how much charge will be left after 3 hours? Solve the equation and graph the battery percentage over time.

• 75%

• 42.19%

• 10%

• 50%