MAT 1235 Calculus II Section 6.5 Exponential Growth and Decay

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Presentation transcript:

MAT 1235 Calculus II Section 6.5 Exponential Growth and Decay

Homework and … WebAssign HW 6.5

Preview The problems from this section are at most at pre-cal level. It was moved, in the 6 th edition, from section 9 to section 7. We will look at how to find the formula in additional to verifying the formula.

Two Common Ways… 2 ways to introduce a mathematical fact… 1. Verification 2. Show (Prove)

Two Common Ways… 2 ways to introduce a mathematical fact… 1. Verification 2. Show (Prove)

Two Common Ways… 2 ways to introduce a mathematical fact… 1. Verification 2. Show (Prove)

Two Common Ways… 2 ways to introduce a mathematical fact… 1. Verification 2. Show (Prove)

Definitions Differential Equation (D.E.): An equation involves derivatives Initial Value Problem (IVP): A D.E. with an initial condition Section 9

Example 1 D.E. IVP

Theorem The solution of is where c is some constant.

Solutions In addition to verification as done in the book, we are going to look at how to actually show that there are no more solutions.

Verification

Separable Equations (10.3)

Application Examples Elementary, at pre-cal level.

Population Model: Unlimited Growth

Example2

Radioactive Decay

Example 3