Chapter 3 Section 4 MA1032 Data, Functions & Graphs Sidney - - PowerPoint PPT Presentation

Chapter 3 Section 4

MA1032 Data, Functions & Graphs Sidney Butler

Michigan Technological University

October 11, 2006

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The number e Why?

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Interchanging with the old

1 Q(t) = abt now in light of e. 2 Annual effective growth factor 3 Continuous growth rate S Butler (Michigan Tech) Chapter 3 Section 4 October 11, 2006 3 / 9

Example

Suppose that a lake is evaporating at a continuous rate of 3.5% per month. Find a formula that gives the amount of water remaining after t months. Determine what percentage the amount of water decreases each month.

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e as a function

y = f (x) = ex

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Compound Interest P0

• 1 + r

n n

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Continuous Growth & Compound Interest

Suppose a nominal interest rate of 20% is being compounded many times per year. Number of compounding periods Growth Factor 10 100 1000 10000

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Example

Suppose that $500 is invested in an account earning 8% compounded continuously.

1 What is the effective annual rate? 2 Find a formula that gives the amount of money in the account after t

years.

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Summary

1 The number e 2 Continuous growth rates 3 Compound interest S Butler (Michigan Tech) Chapter 3 Section 4 October 11, 2006 9 / 9