
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?

$\displaystyle f(t) = \dfrac{83000}{1+2074e^{1.6t}}$
Put t = 8 (Smile)

http://www.mathhelpforum.com/mathhe...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

Yes, and the tabs are [tex] and not [code] (Giggle)

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

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.

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.

$\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

Quite.
You missed a zero.
$\displaystyle f(t) = \dfrac{83000}{1+2074(0.00000276)}$
$\displaystyle f(t) = \dfrac{83000}{1+0.00572}$

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

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.

thanks again for all the help u have given me