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)

Question

Responses

$40.96
$40.96

$6.30
$6.30

$81.92
$81.92

$5.85

Answer 1

To find out how much money the father gives his son on day 14, we can use the pattern established in the problem. The amount given on each day is doubled compared to the previous day.

The money given on each day is as follows:

• Day 1: $0.01 (which is \(2^0 \times 0.01\))
• Day 2: $0.02 (which is \(2^1 \times 0.01\))
• Day 3: $0.04 (which is \(2^2 \times 0.01\))
• Day 4: $0.08 (which is \(2^3 \times 0.01\))

Continuing this pattern, on Day \(n\), the amount is calculated as:

\[ \text{Amount on Day } n = 0.01 \times 2^{(n-1)} \]

For Day 14:

\[ \text{Amount on Day 14} = 0.01 \times 2^{(14-1)} = 0.01 \times 2^{13} = 0.01 \times 8192 \]

Now we calculate:

\[ 0.01 \times 8192 = 81.92 \]

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

Therefore, the correct response is:

$81.92