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Rates of change and differential equations — Question 7

QCAA 2023, Paper 1 · 1 mark

Q7 · 2023 · Technology-freeSimple familiar1 mark

QUESTION 7

The differential equation for which the solution is a logistic equation of the form y=ab+Ce−aty=\dfrac{a}{b+Ce^{-at}} where aa, bb and CC are constants is
(A)
dydt=0.25(1−0.01t)\dfrac{dy}{dt}=0.25(1-0.01t)
(B)
dydt=0.25(1−0.01y)\dfrac{dy}{dt}=0.25(1-0.01y)
(C)
dydt=0.25t(1−0.01t)\dfrac{dy}{dt}=0.25t(1-0.01t)
(D)
dydt=0.25y(1−0.01y)\dfrac{dy}{dt}=0.25y(1-0.01y)
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