On day 1, a father gives his son $0.01. On day 2, he gives him $0.02, and on day 3 he gives him $0.04. The father continues to double the amount of money he gives his son each day. How much money does the father give his son on day 14? (1 point) $6.30 $40.96 $5.85 $81.92

Answer 1

The amount of money the father gives his son each day doubles from the previous day.

On day 1, the father gives:

• Day 1: \(0.01 = 2^0 \times 0.01\)

On day 2, the father gives:

• Day 2: \(0.02 = 2^1 \times 0.01\)

On day 3, the father gives:

• Day 3: \(0.04 = 2^2 \times 0.01\)

Continuing this pattern, on day \(n\), the amount given is:

• Day \(n\): \(0.01 \times 2^{(n-1)}\)

For day 14: \[ \text{Amount on day 14} = 0.01 \times 2^{(14-1)} = 0.01 \times 2^{13} \]

Calculating \(2^{13}\): \[ 2^{13} = 8192 \]

So, \[ \text{Amount on day 14} = 0.01 \times 8192 = 81.92 \]

Thus, the father gives his son $81.92 on day 14.