Understanding Exponential Growth and Graphs in Depth

1. A bacteria culture doubles in size every hour. If there are 100 bacteria at the start, how many will there be after 5 hours?

• 1600

• 3200

• 2400

• 4000

2. The table below shows the population of a small town over 4 years. Year 0: 500, Year 1: 750, Year 2: 1125, Year 3: 1687.5. Is the population growing exponentially? Explain your reasoning.

• No, the population is decreasing.

• Yes, the population is stable.

• No, the population is fluctuating.

• Yes, the population is growing exponentially.

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

• $15,000

• $8,000

• $12,500

• $10,240

4. The graph shows the growth of a plant over time. If the plant's height is 2 cm at time 0 and reaches 50 cm at time 5, is this an example of exponential growth? Justify your answer using the graph.

• The plant's height is constant, indicating no growth.

• No, it is not necessarily exponential growth.

• The graph shows a linear increase, which is a form of exponential growth.

• Yes, it is exponential growth because the height increases rapidly.

5. A certain investment grows at a rate of 8% per year. If you invest $1,000, how much will you have after 10 years?

• 2500.00

• 1800.00

• 2000.00

• 2158.92

6. The table below shows the number of views on a viral video over 4 days: Day 1: 200, Day 2: 600, Day 3: 1800, Day 4: 5400. Is this an example of exponential growth? Explain your answer.

• No, this is a linear growth.

• No, the views decreased over time.

• Yes, this is an example of exponential growth.

• Yes, but only for the first two days.

7. A population of rabbits increases by 50% every month. If there are initially 40 rabbits, how many will there be after 4 months?

• 300

• 150

• 80

• 202

8. The graph of a function shows a rapid increase in value after a certain point. What does this indicate about the growth of the function?

• The function's growth is linear and consistent.

• The function is growing rapidly, indicating exponential growth.

• The function is decreasing steadily over time.

• The function has reached its maximum value and will not change.

9. A tree grows at a rate of 10% per year. If the tree is currently 5 feet tall, how tall will it be after 3 years?

• 8.2 feet

• 7.5 feet

• 9.0 feet

• 6.655 feet

10. The table below shows the amount of money in a savings account over 5 years with a 5% annual interest rate: Year 0: $1,000, Year 1: $1,050, Year 2: $1,102.50, Year 3: $1,157.63, Year 4: $1,215.51. Is the growth of the savings account exponential? Explain your reasoning.

• No, the growth is negative.

• Yes, the growth of the savings account is exponential.

• No, the growth is linear.

• Yes, the growth is constant.