ediculeN

2021-01-19

The population of a culture of bacteria is modeled by the logistic equation
$P(t)=\frac{14,250}{1+29e\u20130.62t}$
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

Skilled2021-01-20Added 106 answers

$P(t)=\frac{14,250}{1+29{e}^{(}-0\ast 62t)}$

$Ast\Rightarrow \mathrm{\infty},{e}^{-0\ast 62t}\Rightarrow 0$

$\therefore P(t)\Rightarrow 14,250$.

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

$\Rightarrow \text{\u29f8}14,2501+29{e}^{(-0\ast 62t)}=\frac{3}{4}(\text{\u29f8}14,250)$

$\Rightarrow 1+29{e}^{-0\ast 62t}=\frac{3}{4}$

$\Rightarrow {e}^{(-0\ast 62t)}=\frac{1}{87}$

$\Rightarrow t=\frac{1}{0\ast 62}In(87)=7\cdot 2$

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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