Question

6 exit ticket: would you rather have $1,000,000 or start with a penny and double your money every day for 30 days? answer and explain why you made this choice

Explanation:

Step1: Define the formula for compound growth

The amount of money when starting with a penny (\$0.01) and doubling each day follows the formula for exponential growth: \( A = P \times 2^{n - 1} \), where \( P = 0.01 \) (initial amount), \( n \) is the number of days.

Step2: Calculate the amount after 30 days

Substitute \( n = 30 \) and \( P = 0.01 \) into the formula:
\( A = 0.01 \times 2^{30 - 1} \)
\( 2^{29}=536870912 \)
\( A = 0.01\times536870912 = 5368709.12 \)

Step3: Compare with \$1,000,000

We have \$5,368,709.12 from the penny - doubling option and \$1,000,000 from the other option. Since \( 5368709.12>1000000 \)

Answer:

I would rather start with a penny and double my money every day for 30 days because after 30 days, the amount of money from this option (\$5,368,709.12) is more than \$1,000,000.