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A startup’s user base grows exponentially. On day 0, there are 1,200 users. After 10 days, the base reaches 7,680 users. Assuming continuous exponential growth \( P(t) = P_0 e^{kt} \), what is the approximate number of users after 20 days?
\( P_0 = 1200 \), \( P(10) = 7680 \)
\( 7680 = 1200 e^{10k} \Rightarrow e^{10k} = \frac{7680}{1200} = 6.4 \)
\( 10k = \ln(6.4) \approx 1.856 \Rightarrow k \approx 0.1856 \)
\( P(20) = 1200 e^{0.1856 \times 20} = 1200 e^{3.712} \)
\( e^{3.712} \approx e^{3.7} \approx 40.45 \) (Since \( e^{3.4} \approx 30, e^{3.7} \approx 40.5, e^{3.712} \approx 40.6 \))
\( P(20) \approx 1200 \times 40.6 = 48,720 \)
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An epidemiologist is analyzing vaccination rates across 5 regions. The rates (in %) are: 68, 74, 70, 82, and 76. She wants to compute the standard deviation to assess disparity. What is the standard deviation, rounded to the nearest tenth?
Mean: \( \frac{68 + 74 + 70 + 82 + 76}{5} = \frac{370}{5} = 74 \)
