I'm completely lost on this one; I haven't encountered a question like this before (with two growth rates).
So, there's this experimenter who tosses 4 coins (this is toss 1) and about half of them (2) land with heads up. She adds the amount that landed heads up (2) to the intial number of coins (4) for a total of 6 coins. Then she tosses these 6 coins, and about half of them (3) turn up heads. She adds the 3 to the 6 to start the next (third) toss with 9 coins. This pattern of about 50% of the coins turning up heads continues, and we can look at this as exponential growth, with a growth rate of 50% or 0.5. An exponential equation for this experiment would be:
C=4(1+0.5)^n (where C is the total number of coins at toss n). Ok, I get this so far and came up with the equation myself.
Here's the confusing aspect:
"The experimenter claims that the equation is explained by the formula for compound interest: A=P(1+i)^n. She argues that P represents the number of coins she started with, and i is 0.5 since the growth rate is about 50% (since about one-half of the coins tossed come up heads), and n is the number of tosses, which is like the compounding period. If her hypothesis is correct, create a formula that predicts the total number of coins if an unfair (weighted) coin is used that only comes up heads 1 out of every 4 times."
So here's what I have:
The probability of the unfair coin turning up heads is 25%.
The probability of a regular coin turning up heads is 50%.
What are the next logical steps? How would I go about answering this question? I'm not sure if I even understand it all that well. I'd really appreciate any help. I'm lost. :-(