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

$6.30
$6.30

$5.85
$5.85

$81.92
$81.92

$40.96

Answer 1

On day 1, the father gives his son $0.01, which can be expressed as \( 0.01 = 2^0 \times 0.01 \). Each subsequent day, the amount given is doubled.

The formula for the amount given on day \( n \) is: \[ \text{Amount on day } n = 0.01 \times 2^{(n-1)} \]

For day 14, substitute \( n = 14 \) into the formula: \[ \text{Amount on day 14} = 0.01 \times 2^{(14-1)} = 0.01 \times 2^{13} \]

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

Now, multiply by \( 0.01 \): \[ \text{Amount on day 14} = 0.01 \times 8192 = 81.92 \]

Thus, the amount given on day 14 is $81.92.

The correct response is: $81.92