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.

Answer 1

Hello there! Welcome to QuestionCove!

If you notice, Nadir is saving double the amount every single day. If we graphed this out, we would see that it's exponential.

Day 1: 1
Day 2: 2
Day 3: 4
Day 4: 8
Day 5: 16
and so on

We want to find how much he saves on Day 15. We can do this 2 ways:
a) calculate it manually, so keep on doubling the number by 2 until we reach day 15, or
b) find the pattern and then plug in the day to find how much he raises on a specific day

I'll help you find the pattern.
You already noticed that each time we multiply the previous number by 2.

Here is the general formula
y = a(b)^x

a would be our starting amount
b is how much we keep multiplying the previous number by

We need to modify the equation a bit since we start off with 1 and then multiply by 2 everyday.

y = a(b)^(x-1)

If you see now, plug in your a and b values based on what I said earlier. x will be the day number. y will tell you how much he saved on the day.

Feel free to ask for more clarification, and I'd be more than happy to help you work through with this problem!