Calculate
d
r
/
d
τ
by the chain rule, and then check your result by expressing r in terms of
τ
and differentiating.
r
=
e
t
i
+
4e
−
t
j
;
t
=
τ
2
With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.
Find the differential of the function. u = 3x4 + 4
Find the centroid of the plane area shown below using integration.
y
y²= 3x
y=x²/3
X
Imagine that we can quarantine infected members of the population, so that they are unable to transmit the disease to others. Let q represent the fraction of the infected population which is quarantined, and let 1-q represent the fraction of the infected population that is not quarantined and can transmit the disease to the susceptible individuals. (Please use google sheets)
a. Rewrite the difference equation for S[t+1] and I[t+1] (from question 1), to incorporate the effects of quarantine. (Hint: quarantine should affect the term representing the proportion of susceptible individuals who are interacting with infected each time step)
b. In the model you developed for question 1 implement the fraction of quarantined people by adding (1-q) to the equations for S and I. Show what happens for a quarantine percentage of 50%, meaning that 50% of infectious people are in quarantine and cannot interact with the susceptible. What can you tell about the impact of quarantine.
Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
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