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Solutions Section 1.1
1. The rate of change in the population
is the derivative
. The
Malthusian Growth Law states that the rate of change in the population is
proportional to
. Thus
, where is the proportionality
constant. Without reference to the variable, the diﬀerential equation
becomes
2. a. This statement mathematically is
where we have used
to represent the proportionality constant.
b. This statement translates as
where we have used
to
represent the proportionality constant.
c. The overall growth rate is
. Thus the Logistic Growth Law is 3. Torricelli’s law states that the change in height,
the square root of the height,
. Thus
proportionality constant. is proportional to
, where is the 4. The highest order derivative is
is
. so the order is and the standard form 5. The highest order derivative is
. so the order is . The standard form is 6. The highest order derivative is
is
. so the order is 1 and the standard form ...
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This note was uploaded on 12/22/2011 for the course MAP 2302 taught by Professor Bell,d during the Fall '08 term at UNF.
 Fall '08
 BELL,D

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