# Thread: logistic growth

1. ## 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?

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

Put t = 8

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

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

AM I GOING CORRECT

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

5. is this correct

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

f(t) = \dfrac{83000}{5727}

f(t) = 14.49
$

6. From here... no.

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

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

7. From here... no.

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

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

8. $

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

f(t) = \dfrac{83000}{1+0.0572}

f(t) = \dfrac{83000}{1.06}
$

is this it

9. Quite.

You missed a zero.

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

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

10. $
f(t) = \dfrac{83000}{1.00572}
[br]
f(t) = 82527.9
$

11. 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.

12. thanks again for all the help u have given me