8. Formulate a differential equation that describes each one of the following st

Question

8. Formulate a differential equation that describes each one
of the following statements:
a) A medication is injected into the bloodstream
from a patient to a constant ratio of grams
per second. Simultaneously, the medication
eliminates with a rapidity proportional to the amount
present z at time t.
b) The reason for changing the temperature of a cup of
coffee z at time t is proportional to the difference
between the temperature of the environment M and the
coffee temperature z at time t.
Differential Equations, Task No 1: Basic Concepts of Differential Equations, Type: 7 2
c) The reason for changing the amount of salt z in a
tank at time t is proportional to the square
of the amount of salt present in salt at time t.
d) The speed with which something is memorized is proportional
to the square of the amount of knowledge that
it remains to memorize. Suppose that M is the amount
total of subjects to memorize and that z represents the
amount memorized at time t.
e) The velocity at time t of a particle that is
moves along a straight line is proportional to
the fourth power of its z position.
Indicate the option that contains the differential equation that
model it in the following list. In them k represents
a constant of proportionality.

Explanation / Answer

(a) z' = r - kz

(b) z' = k (M - z)

(c) z' = k (z^2)

(d) z' = k (M - z)^2

(e) z' = k (z^4)

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