richards greenwich
PC//TV/Pad .
//iPad 1. .
//iPad .
-
- IDM Edge 1.Microsoft Edge Tampermonkey .
.
10G
App .
100G .
pc/app,,,,,, AI,,.
iiMedia Research45.9%47.2 ...
Related Articles
Trending Articles
An online learning platform observes that course completion rates follow the logistic model \( C(t) = \frac{1000}{1 + 9e^{-0.2t}} \), where \( C(t) \) is the number of completions after \( t \) weeks. After how many weeks does the number of completions first exceed 900?
Solve \( \frac{1000}{1 + 9e^{-0.2t}} > 900 \)
Divide both sides:
\frac{1000}{900} > 1 + 9e^{-0.2t} \Rightarrow \frac{10}{9} > 1 + 9e^{-0.2t}
\frac{10}{9} - 1 > 9e^{-0.2t} \Rightarrow \frac{1}{9} > 9e^{-0.2t}
\frac{1}{81} > e^{-0.2t}
Take natural log:
\ln\left(\frac{1}{81}\right) > -0.2t \Rightarrow -\ln(81) > -0.2t
\ln(81) < 0.2t
\( \ln(81) = \ln(3^4) = 4\ln(3) \approx 4 \times 1.0986 = 4.3944 \)