logistic growth

**math321** · November 19th 2010, 07:02 AM

i really dont no what the hell to do for this question

can some1 guide me tru this 1

The logistic growth function
f(t) = (83,000 ) / 1 + 2074e^-1.6t

models the number of people who have become ill with a
particular infection t weeks after its initial outbreak in a particular community. How many people were ill after
8 weeks?

**Unknown008** · November 19th 2010, 07:07 AM

$f(t) = \dfrac{83000}{1+2074e^{-1.6t}}$

Put t = 8

**math321** · November 19th 2010, 08:42 AM

therefore
$ f(t) = \dfrac{83000}{1+2074e^{-1.6(8)}} f(t) = \dfrac{83000}{1+2074e^{-12.8}} $

AM I GOING CORRECT

**Unknown008** · November 19th 2010, 08:44 AM

Yes, and the tabs are [tex] and not [code]

**math321** · November 19th 2010, 08:50 AM

is this correct

$ f(t) = \dfrac{83000}{(1+2074)(2.76)} f(t) = \dfrac{83000}{5727} f(t) = 14.49 $

**Unknown008** · November 19th 2010, 08:57 AM

From here... no.

$e^{-12.8} = 2.76 \times 10^{-6}$

This multiplied by 2074 will give a very small number, less than 1.

**math321** · November 19th 2010, 09:00 AM

From here... no.

$e^{-12.8} = 2.76 \times 10^{-6}$

This multiplied by 2074 will give a very small number, less than 1.

**math321** · November 19th 2010, 09:06 AM

$ f(t) = \dfrac{83000}{1+2074(0.0000276)} f(t) = \dfrac{83000}{1+0.0572} f(t) = \dfrac{83000}{1.06} $

is this it

**Unknown008** · November 19th 2010, 09:10 AM

Quite.

You missed a zero.

$f(t) = \dfrac{83000}{1+2074(0.00000276)}$

$f(t) = \dfrac{83000}{1+0.00572}$

**math321** · November 19th 2010, 09:13 AM

$ f(t) = \dfrac{83000}{1.00572} [br] f(t) = 82527.9 $

**Unknown008** · November 19th 2010, 09:20 AM

This should be okay

When I input this in my calculator, I get:

$f(t) = \dfrac{83000}{1+2074e^{-1.6(8)}} = 82527.46077...$

It's fairly close since you too the approximation of the exponential.

**math321** · November 19th 2010, 09:36 AM

thanks again for all the help u have given me

Thread: logistic growth

LinkBack

Thread Tools

Display

logistic growth

Similar Math Help Forum Discussions

logistic growth equation

Logistic Growth

logistic growth problem

logistic growth models

Derive Logistic Growth Equation

Search Tags