Respuesta :
Answer:
[tex] x= -\frac{ln [\frac{5P}{8000-P}]}{0.002}[/tex]
a) [tex] x= -\frac{ln [\frac{5*200}{8000-200}]}{0.002} =1027.062 \approx 1027[/tex]
b) [tex] x= -\frac{ln [\frac{5*800}{8000-800}]}{0.002} =293.893 \approx 294[/tex]
Step-by-step explanation:
For this case we have the following function:
[tex] P= 8000 (1- \frac{5}{5 +e^{-0.002 x}})[/tex]
We can solve for x like this. First we can reorder the expression like this:
[tex] \frac{P}{8000} = 1- \frac{5}{5+e^{-0.002x}}[/tex]
[tex] \frac{5}{5+e^{-0.002x}} = 1 -\frac{P}{8000} = \frac{8000-P}{8000}[/tex]
[tex] \frac{40000}{8000-P} = 5 + e^{-0.002x}[/tex]
Now we can apply natura log on both sids and we got:
[tex] ln[\frac{40000}{8000-P} -5] = ln e^{-0.002x}[/tex]
[tex] ln [\frac{5P}{8000-P}] = -0.002x [/tex]
And if we solve for x we got:
[tex] x= -\frac{ln [\frac{5P}{8000-P}]}{0.002}[/tex]
Part a
For this case we can replace P = 200 and see what we got for x like this:
[tex] x= -\frac{ln [\frac{5*200}{8000-200}]}{0.002} =1027.062 \approx 1027[/tex]
Part b
For this case we can replace P = 800 and see what we got for x like this:
[tex] x= -\frac{ln [\frac{5*800}{8000-800}]}{0.002} =293.893 \approx 294[/tex]
