Question

Nadir saves $1 the first day of a month, $2 the second day, $4 the third day, and so on. He continues to double his savings each day. Find the amount that he will save on the fifteenth day.

Question 3 options:

$16,384

$29

$32,768

$8192

Answer 1

$16,384

Explanation:

The amount of money Nadir saves increases exponentially by a factor of 2. If you keep multiplying each previous number by 2 until you get to the 15th number, (2*2, 4*2, 8*2, 16*2), you will get 16,384.

Answer 2

$16,384

Explanation:

Let's find the general equation for his savings:

The first day he saves $1 =
`2^(0)`

The second day, $2 = 1*2 =
`2^(1)`

The third day, $4 = 1*2*2 =
`2^(2)`

The fourth day, $8 = 1*2*2*2 =
`2^(3)`

In general, in the n-th day, he saves
`2^(n-1)`

With this, we can calculate the amount that he will save on the fifteenth day:

`2^(15-1) = 2^(14) = \$16,384`