Exponential Functions Test Review Test Date 30 Mar

Exponential Functions Test Review Test Date – 30 Mar 2011

Parts of Exponentials y = a(b)x • Base – a - the number or expression being raised to a power; the value in parenthesis • Exponent – x - the power the base is raised to; the small raised number or expression • Initial Value – a - the value when the exponent is zero; the y-intercept; the number outside parenthesis

Parts of Exponentials Identify the base, exponent, and initial value y = 3(2)2 t y = 10, 000( ½ )3 y = 0. 8(1. 25)x+3

Parts of Exponentials Identify the base, exponent, and initial value y = 3(2)2 t y = 10, 000( ½ )3 y = 0. 8(1. 25)x+3 Base: 2 ½ 1. 25

Parts of Exponentials Identify the base, exponent, and initial value y = 3(2)2 t y = 10, 000( ½ )3 y = 0. 8(1. 25)x+3 Base: 2 ½ 1. 25 Exponent: 2 t 3 x+3

Parts of Exponentials Identify the base, exponent, and initial value y = 3(2)2 t y = 10, 000( ½ )3 y = 0. 8(1. 25)x+3 Base: 2 ½ 1. 25 Exponent: 2 t 3 x+3 Initial Value: 3 10, 000 0. 8

Evaluating Exponentials • Raise the base to the power before multiplying or adding anything else. Evaluate: y = 3(2)2 y = 500(. 8)4

Evaluating Exponentials • Raise the base to the power before multiplying or adding anything else. Evaluate: y = 3(2)2 y = 3(4) y = 12 y = 500(. 8)4 y = 500(. 4096) y = 204. 8

Growth vs. Decay • Functions that go up as x or t increases are exponential growth functions – growth occurs if the base b > 1 – asymptote is y = 0, for x < 0 • Functions that go down as x or t increases are exponential decay functions – decay occurs if the base b < 1 – asymptote is y = 0, for x > 0

Growth (or Decay) Rate • The growth rate is: – r=b-1 • This works for decay – b < 1 so r is negative • Remember!! – r is a decimal value – If you have a percentage, to find r you must divide by 100

Examples Write the function equation: 1) Initial value = 100, growth rate = 5% 2) y-intercept = 5, decay rate = 25% 3) Initial value = 0. 05, base = 10

Examples Write the function equation: 1) Initial value = 100, growth rate = 5% 2) y-intercept = 5, decay rate = 25% 3) Initial value = 0. 05, base = 10 1) y = 100(1. 05)x 2) y = 5(0. 75)x 3) y = 0. 05(10)x

Graphing Exponentials • Find the value for x = 0 (remember: any number raised to the zero power = _____)

Graphing Exponentials • Find the value for x = 0 (remember: any number raised to the zero power = 1) • Make a table for values near 0 (x = -2, -1, 1, 2, …) • Be sure the trend makes sense (growth vs. decay) • Plot the points on a graph.