Zadanie 2a
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Show that .
Hence or otherwise solve log3[x(x2 − 4)] − 1 = log3[(x2 − 11x + 18)(x + 2)].
A field team has 12 specialists. Select an eight-person deployment group with three distinct roles: navigation lead, equipment lead and communications lead; the other five members have no assigned roles. How many selections are possible?
For the logistic model: (i) interpret choosing L=1000; (ii) find C; (iii) find k; (iv) predict the membership count at t=8, to the nearest whole member.
For the Gompertz model: (i) state dx/dt at x=1000; (ii) interpret it; (iii) for h(x) = ln(ln 1000 − ln x),0<x<1000, show h′(x) = −1/[xln(1000/x)]; (iv) hence separate variables to show ln x = ln 1000 − Ae−at with A>0; (v) find A as ln p for a positive…
Compare the two predictions with the t=8 audit.
The adjusted model is dx/dt = .101xln(1000/x) − .01x. (i) Starting at x₀=250 when t=4, use Euler’s method with step 0.4 years to estimate the count at t=8, to the nearest whole member. (ii) Comment on this prediction.
Find .
Find P(A ∣ B′).
Explain why the median of all 26 masses remains 18 g.