Goldstein/Schneider/Lay/Asmar, CALCULUS AND ITS APPLICATIONS, 11e – Slide 1 of 78 § 0.5 Exponents and Power Functions.

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Presentation transcript:

Goldstein/Schneider/Lay/Asmar, CALCULUS AND ITS APPLICATIONS, 11e – Slide 1 of 78 § 0.5 Exponents and Power Functions

Goldstein/Schneider/Lay/Asmar, CALCULUS AND ITS APPLICATIONS, 11e – Slide 2 of 78  Exponent Rules  Applications of Exponents  Compound Interest Section Outline

Goldstein/Schneider/Lay/Asmar, CALCULUS AND ITS APPLICATIONS, 11e – Slide 3 of 78 Exponents DefinitionExample

Goldstein/Schneider/Lay/Asmar, CALCULUS AND ITS APPLICATIONS, 11e – Slide 4 of 78 Exponents DefinitionExample

Goldstein/Schneider/Lay/Asmar, CALCULUS AND ITS APPLICATIONS, 11e – Slide 5 of 78 Exponents DefinitionExample

Goldstein/Schneider/Lay/Asmar, CALCULUS AND ITS APPLICATIONS, 11e – Slide 6 of 78 Exponents DefinitionExample

Goldstein/Schneider/Lay/Asmar, CALCULUS AND ITS APPLICATIONS, 11e – Slide 7 of 78 Exponents DefinitionExample

Goldstein/Schneider/Lay/Asmar, CALCULUS AND ITS APPLICATIONS, 11e – Slide 8 of 78 Applications of ExponentsEXAMPLE SOLUTION Use the laws of exponents to simplify the algebraic expression. This is the given expression.

Goldstein/Schneider/Lay/Asmar, CALCULUS AND ITS APPLICATIONS, 11e – Slide 9 of 78 Applications of ExponentsCONTINUED Subtract. Divide.

Goldstein/Schneider/Lay/Asmar, CALCULUS AND ITS APPLICATIONS, 11e – Slide 10 of 78 Compound Interest - Annual DefinitionExample Compound Interest Formula: A = the compound amount (how much money you end up with) P = the principal amount invested i = the compound interest rate per interest period n = the number of compounding periods If $700 is invested, compounded annually at 8% for 8 years, this will grow to: Therefore, the compound amount would be $1,

Goldstein/Schneider/Lay/Asmar, CALCULUS AND ITS APPLICATIONS, 11e – Slide 11 of 78 Compound Interest - General

Goldstein/Schneider/Lay/Asmar, CALCULUS AND ITS APPLICATIONS, 11e – Slide 12 of 78 Compound Interest - GeneralEXAMPLE SOLUTION (Quarterly Compound) Assume that a $500 investment earns interest compounded quarterly. Express the value of the investment after one year as a polynomial in the annual rate of interest r. Since interest is not being compounded annually, we must use this formula. Replace P with 500, m with 4 (interest is compounded 4 times each year), and t with 1 (interest is being compounded for 1 year). Simplify.