Page 16 - Calculus for the Clueless, Calc II
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Chapter 4—
Exponential Growth and Decay
In every book on calculus, there is a little on differential equations, which are equations with derivatives.
Usually, one chapter is devoted to this topic, which is almost never used. Parts of one or two other chapters may
have differential equations in them. This topic is almost universally covered by all courses.
Example 1—
The rate of change of marlenium is proportional to the amount.
Ten pounds of marlenium become 90 pounds in 4 hours.
A. Write the equation.
B. How many pounds of marlenium will there be in 10 hours?
C. When will there be 500 pounds of marlenium?
1A. The differential equation to solve is dM/dt = kM where k is a konstant.
We solve this by separation of variables.
Integrate.
We need a trick. Let C = ln M o
where M o = the amount of marlenium at t = 0.
By law 6 of logs,
By the definition of logs,
Divide by 10
Take Ins
