Question

Remember, purse A starts with $1,000 and grows by $200 each day. Purse B starts with $0.01 and doubles each.

1. Purse A will always have more money.
2. Purse B will surpass Purse A after a certain number of days.
3. Purse A and Purse B will have the same amount after a certain number of days.
4. Purse B will always have more money.

Answer 1

Purse A increases at a linear rate while Purse B grows at an exponential rate. Initially, Purse A has more money, but due to compound growth, Purse B will surpass Purse A after a certain number of days.

Step-by-step explanation:

The question involves a mathematical comparison between two different ways of increasing money over time. Purse A starts with a $1,000 balance and increases by $200 each day, whereas Purse B starts with $0.01 and doubles each day.

To determine which purse will eventually have more money, we need to create an equation or model for each purse and then calculate over time. For example, Purse A can be modeled by the equation A = 1000 + 200d, where 'd' is the number of days that have passed. Purse B, on the other hand, has a growth model of B = 0.01 × 2^d.

Comparing these two, Purse A grows at a linear rate, while Purse B grows at an exponential rate. Initially, Purse A has more money, but there will come a day when Purse B's exponential growth surpasses the linear growth of Purse A. Thus, the correct answer would be that Purse B will surpass Purse A after a certain number of days. This demonstrates the power of compound interest and growth over time.