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Math 140. 4.1 – Exponential Functions; Continuous Compounding. Some things just don’t grow linearly, they grow exponentially (ex: population, compound interest ). Some things just don’t grow linearly, they grow exponentially (ex: population, compound interest ). U.S. Population.

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math 140

Math 140

4.1 – Exponential Functions; Continuous Compounding

slide2

Some things just don’t grow linearly, they grow exponentially (ex: population, compound interest).

slide3

Some things just don’t grow linearly, they grow exponentially (ex: population, compound interest).

U.S. Population

Source: http://en.wikipedia.org/wiki/File:US_Population,_1790_-_2011.svg

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Natural Exponential Base:

(Amount of money you’d have in an account if you invested $1 at 100% interest rate per year for one year, where interest is compounded continuously.)

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In general, the continuously compounded interest formula is , and the regular compound interest formula is .

slide8

Ex 1.

Evaluate:

Ex 2.

Solve:

Ex 3.

Solve:

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Ex 4.

Find values of the constants and so that the curve contains and .

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Ex 4.

Find values of the constants and so that the curve contains and .