If you received a penny a day and the amt doubled every week how long would it take to get a million dollars?

Answer 1

This question need to be clarified.

The question, as is, is saying:

After one week, you have $.07. Double this to get $.14 Seven more days pass. Since you get a penny a day, you now have $.21. Double this to get $.42.

Seven more days pass. Since you get a penny a day, you now have $.49. Double this to get $.98.

Rather, more likely I think the person is asking: "If you received a penny on the first day, and each day after your amount doubles, after how many days would you have a million dollars?"

The formula to figure out the amount at a particular day n is:

$.01 * 2n-1 = amount on day n

So, for example:

on day 1, you have:

$.01 * 20, which equals $.01

on day 2, you have:

$.01 * 21, which equals $.02

To find the answer about the million dollars, we can look at the equation as:

$.01 * 2n-1 > $1,000,000

Now, divide each side by .01, to get:

2n-1 > 100,000,000

Represent the right side as an exponent: 2n-1 > 108

Now, find the logarithm of each side, to get: (n-1)(log 2) > (8)(log 10)

log 10 equals 1, so we get: (n-1)(log 2) > 8 Divide each side by log 2: n-1 > (8)/(log 2) Log 2 equals .3, so

n-1 > 26.6 Add 1 to each side:

n > 27.6 This tells us that the number of days to get $1M is greater than 27.6 days. So, at the 27th day, we would not yet have $1M, but on the 28th day, we would.

Answer: 28 days.