Separable Differential Equations Worksheets Page 5
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7Calculus Maximus
Notes 5.1: Separable Diff EQ
Example 8:
dA
= kA , where t is
An amount, A, increases at a rate proportional to its current amount, such that
dt
measured in hours. If the amount triples every 11 hours, find the value of k (both exact and 3-decimal
approximation).
Example 9:
226
Radium-226 (
Ra ) loses its mass at a rate that is directly proportional to its mass. If its half-life is 1590
88
years, and if we start with a sample of radium-226 with a mass of 100 mg,
(a) Find the formula for the mass,
M t that remains after t years.
(b) How many mg of the original sample remains after 100 years?
(c) How many years (exact answer) will it take for the sample to have only 3 mg remaining?
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