# Interpret success-rate/time * $#### McFluffy 1. Homework Statement You are applying for a $\1000$ scholarship and your time is worth $\10$ an hour. If the chance of success is $1 -(1/x)$ from $x$ hours of writing, when should you stop? 2. Homework Equations Let $p(x)=1 -(1/x)$ be the rate of success as a function of time, $x$. 3. The Attempt at a Solution My way if thinking eventually led to the correct answer which is $\frac{1}{x^2}1000=10$. Solving for $x$ gives you the solution. I was stuck at this problem and didn't know how to proceed and I tried to find out if I could find the answer just by matching up the units on both sides. I don't know how they calculated $p(x)$ but I do know that it is dimensionless. Thus, $p'(x)$ will give me the rate of success per unit time or just the unit, $1/h$. I know that $\1000$ has dollar units and that $10\frac{}{h}$ has dollar per hour unit, so if I multiply $p'(x)=\frac{1}{x^2}$ with $\1000$ I should get the same units as $10\frac{}{h}$. So I set $\frac{1}{x^2}1000=10$ and solved for $x$. Feeling doubtful, I checked the solution and was surprised how I got it right. My question is how do you interpret the solution, $\frac{1}{x^2}1000=10$? Like since $p'(x)$ is defined as the success rate per unit time, how come if I multiplied it by $\1000$, it got me the solution? I just don't understand it, $$\frac{\text{success rate}}{\text{time}}\cdot \text{currency}$$ How do you interpret this? and yes, I'm aware that the success rate is dimensionless but still, I don't understand the reasoning behind the answer. I just want someone to solve the problem with also providing some commentary on his/her methods of solving it as I felt that my reasoning is inadequate. Related Calculus and Beyond Homework Help News on Phys.org #### kuruman Science Advisor Homework Helper Gold Member The more hours you work on the application the better your chance in getting the$1000 scholarship. What is the extra dollars you expect to gain when you spend an extra hour on that application? When those expected extra dollars per hour are equal to your hourly wage of $10, then you must stop working on the application and go flip burgers or whatever. That's what the equation you discovered is saying. BTW, $p(x)$ as given is not dimensionless if $x$ in the denominator has units of hours. #### McFluffy BTW, $p(x)$ as given is not dimensionless if $x$ in the denominator has units of hours. $p(x)$ is the rate of success function, which calculates the probability of being successful, you're referring to $p'(x)$. #### McFluffy The more hours you work on the application the better your chance in getting the$1000 scholarship.
This one I understand as this is how $p(x)$ was defined.