ediculeN

2021-01-19

The population of a culture of bacteria is modeled by the logistic equation $P\left(t\right)=\frac{14,250}{1+29e–0.62t}$ To the nearest tenth, how many days will it take the culture to reach 75% of it’s carrying capacity? What is the carrying capacity? What are the virtues of logistic model?

hesgidiauE

$P\left(t\right)=\frac{14,250}{1+29{e}^{\left(}-0\ast 62t\right)}$
$Ast⇒\mathrm{\infty },{e}^{-0\ast 62t}⇒0$
$\therefore P\left(t\right)⇒14,250$.

$P\left(t\right)=\frac{3}{4}\left(14,250\right).$

$⇒\text{⧸}14,2501+29{e}^{\left(-0\ast 62t\right)}=\frac{3}{4}\left(\text{⧸}14,250\right)$
$⇒1+29{e}^{-0\ast 62t}=\frac{3}{4}$
$⇒{e}^{\left(-0\ast 62t\right)}=\frac{1}{87}$
$⇒t=\frac{1}{0\ast 62}In\left(87\right)=7\cdot 2$

The amount of resources available limits the expansion of any population. An exponential growth model, which only functions in ideal circumstances and is ineffective for simulating real-world scenarios, is preferable to a logistic S curve for simulating this.

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