Integral of the Reciprocal Function:  6-1—Why we need it.  6-2—What it can’t be.  6-2—What it could be.  6-3—By definition it is:  How we can use it.

By the end of today, you will: Practice logarithm properties Find derivatives of functions involving ln Find integrals of reciprocal functions Solve a relevant population problem

the big problem: The more people in a community, the more babies are born per year. Assume that a small town has a population of P = 1000 people now and that the population is growing at an instantaneous rate of 5% per year. This is called a differential equation. You solve these problems with the three I’s Interpret Isolate Integrate

What it can’t be. Let’s try to solve this using the power rule:

What it could be. Look at the sketch in Foerster’s book on page 252 x g(x) Use this table to answer problems 5 and 6 from Foerster’s book on page

By definition it is…

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(Page 259 #20)

(Page 260 # 36)

(Page 260 # 44)

the big problem; what’s the population in year 10?