what total amount is greater: $3.00 tripling each week for 4 weeks or $4.00, quadrupling each week for 3 weeks

3 + 9 + 27 + 81 = ?

4 + 16 + 64 = ?

check to be sure you don't want

3 + 9 + 27 + 81 + 243

4 + 16 + 64 + 256

To calculate the total amounts for each scenario, we can use the formula for compound interest:

A = P(1 + r)^n

Where:
A = the final amount
P = the initial amount
r = the growth rate
n = the number of compounding periods

Let's calculate the total amount for each scenario step by step:

1. Option 1: $3.00 tripling each week for 4 weeks

Initial amount (P) = $3.00
Growth rate (r) = 3 (since it's tripling)
Number of compounding periods (n) = 4

Using the formula, we get:

A = $3.00 * (1 + 3)^4
A = $3.00 * (1 + 81)
A ≈ $3.00 * 82
A ≈ $246.00

So, the total amount after 4 weeks would be approximately $246.00.

2. Option 2: $4.00 quadrupling each week for 3 weeks

Initial amount (P) = $4.00
Growth rate (r) = 4 (since it's quadrupling)
Number of compounding periods (n) = 3

Using the formula, we get:

A = $4.00 * (1 + 4)^3
A = $4.00 * (1 + 64)
A ≈ $4.00 * 65
A ≈ $260.00

So, the total amount after 3 weeks would be approximately $260.00.

Comparing the two scenarios, we can see that $260.00 (quadrupling each week for 3 weeks) is greater than $246.00 (tripling each week for 4 weeks). Therefore, the total amount of $4.00, quadrupling each week for 3 weeks, is greater.