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I have a problem where I found the percentage of cells as time approaches infinity to be $\frac{100d}{c+d}$. All parameters are positive constants. The question asks are there circumstances when this quantity can be zero? I think if $d$ is small and $c$ is large, the percentage is very close to zero. But if all parameters are positive is it true that the quantity can never actually be zero?

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  • $\begingroup$ Even if only $d > 0$ the percentage must be nonzero since a fraction is equal to zero exactly when the numerator is $0$. $\endgroup$ – nbritten Dec 6 '19 at 23:37
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Yes, it is true that if $c,d > 0$, then $\frac{100d}{c+d} > 0$ (so it can't equal $0$).

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    $\begingroup$ would you mind if I delete this problem? $\endgroup$ – user707991 Dec 6 '19 at 23:38
  • $\begingroup$ I wouldn't mind. (Not sure if others would mind though.) $\endgroup$ – Minus One-Twelfth Dec 6 '19 at 23:39
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    $\begingroup$ @user707991 Why are you deleting it? $\endgroup$ – Don Thousand Dec 6 '19 at 23:41
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We have that

$$\frac{100d}{c+d}=0 \iff d=0$$

and

$$\lim_{d/c\to 0} \frac{100d}{c+d}=0$$

$$\lim_{c/d\to \infty} \frac{100d}{c+d}=0$$

and you are right since all quantities are positive the ratio can't never be zero.

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  • $\begingroup$ would you mind if I delete this problem? $\endgroup$ – user707991 Dec 6 '19 at 23:39
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    $\begingroup$ No it is not aproblem of course, since you are asking that! Bye $\endgroup$ – user Dec 6 '19 at 23:40

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