# logistic growth

• Nov 19th 2010, 07:02 AM
math321
logistic growth
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?
• Nov 19th 2010, 07:07 AM
Unknown008
$\displaystyle f(t) = \dfrac{83000}{1+2074e^{-1.6t}}$

Put t = 8 (Smile)
• Nov 19th 2010, 08:42 AM
math321
http://www.mathhelpforum.com/math-he...d0d8c99cd1.png

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

AM I GOING CORRECT
• Nov 19th 2010, 08:44 AM
Unknown008
Yes, and the tabs are [tex] and not [code] (Giggle)
• Nov 19th 2010, 08:50 AM
math321
is this correct

$\displaystyle f(t) = \dfrac{83000}{(1+2074)(2.76)} f(t) = \dfrac{83000}{5727} f(t) = 14.49$
• Nov 19th 2010, 08:57 AM
Unknown008
From here... no.

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

This multiplied by 2074 will give a very small number, less than 1.
• Nov 19th 2010, 09:00 AM
math321
From here... no.

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

This multiplied by 2074 will give a very small number, less than 1.
• Nov 19th 2010, 09:06 AM
math321
$\displaystyle f(t) = \dfrac{83000}{1+2074(0.0000276)} f(t) = \dfrac{83000}{1+0.0572} f(t) = \dfrac{83000}{1.06}$

is this it
• Nov 19th 2010, 09:10 AM
Unknown008
Quite.

You missed a zero.

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

$\displaystyle f(t) = \dfrac{83000}{1+0.00572}$
• Nov 19th 2010, 09:13 AM
math321
$\displaystyle f(t) = \dfrac{83000}{1.00572} [br] f(t) = 82527.9$
• Nov 19th 2010, 09:20 AM
Unknown008
This should be okay (Smile)

When I input this in my calculator, I get:

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

It's fairly close since you too the approximation of the exponential.
• Nov 19th 2010, 09:36 AM
math321
thanks again for all the help u have given me