Analyzing Exponential Growth: Bacteria, Plants, and Value

1. A bacteria culture doubles in size every hour. If the initial population is 100, how many bacteria will there be after 5 hours?

• 4000

• 2400

• 3200

• 1600

2. The table below shows the population of a city over 4 years. Analyze the data and determine the growth factor. Year: 0, Population: 5000; Year: 1, Population: 7500; Year: 2, Population: 11250; Year: 3, Population: 16875. What is the growth factor?

• 1.75

• 2.0

• 1.5

• 1.2

3. A car's value decreases exponentially over time. If the car is worth $20,000 now and loses 15% of its value each year, what will its value be after 3 years?

• $12,282.50

• $10,000

• $18,000

• $15,000

4. The graph shows the growth of two different plants over time. Plant A grows according to the function f(t) = 100(1.5)^t and Plant B grows according to g(t) = 80(1.6)^t. After how many years will Plant B surpass Plant A?

• 5

• 6

• 8

• 7

5. A bank offers an account that compounds interest annually at a rate of 5%. If you deposit $1,000, how much will you have after 10 years? Use the formula A = P(1 + r)^t.

• 2000.00

• 1628.89

• 1500.00

• 1200.50

6. The table below shows the amount of money in an investment account over 4 years. Analyze the data to find the annual growth rate. Year: 0, Amount: $1,000; Year: 1, Amount: $1,200; Year: 2, Amount: $1,440; Year: 3, Amount: $1,728. What is the growth rate?

• 20.50%

• 15.00%

• 12.75%

• 18.20%

7. A certain species of fish in a lake grows exponentially. If there are currently 200 fish and the population triples every year, how many fish will there be in 4 years?

• 4000

• 600

• 8000

• 16200

8. The graph of an exponential function shows a rapid increase. If the function is modeled by y = 2^x, what is the value of y when x = 6?

• 32

• 128

• 256

• 64

9. A smartphone's battery life decreases exponentially. If it starts with a full charge of 100% and loses 20% of its charge every hour, what will the battery percentage be after 3 hours?

• 75%

• 51.2%

• 60%

• 40%

10. A company’s revenue is modeled by the function R(t) = 500(1.1)^t, where t is the number of years since the company started. What will the revenue be after 5 years?

• 750.50

• 805.26

• 600.00

• 900.00