SOLUTION: I stuck on this problem and have been for a while. I hope you can help me out!! A quiz program gives a prize of $5 for teh first question answered correctly. The contestant's pr

Question 122541: I stuck on this problem and have been for a while. I hope you can help me out!!
A quiz program gives a prize of $5 for teh first question answered correctly. The contestant's prize winnings are doubled for each question after the first. How many questions would you need to answer to exceed $1,000,000 in total prize money?

Found 2 solutions by Fombitz, stanbon:
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
This looks like exponential growth.
The formula for exponential growth is

We just need to determine and

So, what is t so that f(t)>1000000

The first time would be the 19th correct question.
For 19 correct answers, you would win

The payout would be $1.307,059.78.

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A quiz program gives a prize of $5 for the first question answered correctly. The contestant's prize winnings are doubled for each question after the first. How many questions would you need to answer to exceed $1,000,000 in total prize money?
5,10,20,40,80,160....
This is a geometric sequence with r=2 and a=5
---------
Sum Formula:
S(n) = a[1-r^(n)]/[1-r]
Example:
S(2) = 5[1-2^(2)]/[1-2] = 5-3/-1 = 15
-------------
Your Problem:
1,000,000 = 5[(2^x)-1]/(2-1)
200,000 = (2^x)-1
200,001 = 2^x
Take the log of both sides to get:
x*log2 = log 200,001
x = [log200,001]/[log2]
x = 17.6096
-----------
When you answer 18 correctly you will be above 1 million in earnings.
==============
Cheers,
Stan H.

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