Chapter 7 Algebra II Review JEOPARDY Jeopardy Review

Logarithms Exponential Growth and Decay Exponential Functions Solving Logarithmic Equations Solving Exponential Equations 200 200 200 400 400 400 600 600 600 800 800 800 1000 1000

Logarithms 200 log 3 (1/9) = A: -2 Jeopardy Review

Logarithms 400 log. 001 A: -3 Jeopardy Review

Logarithms 600 Use the change of base formula to evaluate: log 6 21 A: 1. 699 Jeopardy Review

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Logarithms 800 Using the properties of logarithms, expand log (x 2 y/z) A: 2 log x + log y – log z Jeopardy Review

Logarithms 1000 Write as a single logarithm: y = 4 log m + 2 log n – 3 log k A: log (m 4 n 2/k 3) S 2 C 13 Jeopardy Review

Exponential Growth & Decay 200 Identify the percent of decay in the equation: y = 6000 (. 48)x A: 52% S 2 C 13 Jeopardy Review

Exponential Growth & Decay 400 Write the equation that models exponential growth of 6% per year with a starting population of 22, 000. A: y = 22, 000 (1. 06)x S 2 C 13 Jeopardy Review

Exponential Growth & Decay 600 Predict the population in the year 2006 if a countries population (in millions) is growing by 4% each year, and is modeled by the equation y = 1. 4 (1. 04)x where x represents the years after 1990. A: 2. 62 million S 2 C 13 Jeopardy Review

Exponential Growth & Decay 800 A city’s population is modeled by the equation y = 14, 000 (. 98)x, where x represents the number of years after the year 2000. Predict during which year the population will decrease to 8, 900. A: 2022 S 2 C 13 Jeopardy Review

Exponential Growth & Decay 1000 In the equation: y = 13 (2. 58)x, Identify a) Growth or decay b) Growth or decay factor c) Percent of growth or decay A: a) growth b) 2. 58 c) 158% S 2 C 13 Jeopardy Review

Exponential Functions 200 Evaluate y = 2 x for x = -1, 0, and 2. A: y = ½, 1, and 4 S 2 C 13 Jeopardy Review

Exponential Functions 400 Write the equation to describe the exponential function with a base of 2, passing through the point (4, 7). A: y = (7/16)(2)x S 2 C 13 Jeopardy Review

Exponential Functions 600 Find the amount of money you have if you invest $20, 000 for 5 years at 6% compounded continuously. A: 20, 000 e^(. 06*5) = $26, 977. 18 S 2 C 13 Jeopardy Review

Exponential Functions 800 Find the amount of money you have if you invest $3000 for 3 years at 5% compounded continuously. A: 3000 e (. 05)(3) = $3485. 50 S 2 C 13 Jeopardy Review

Exponential Functions 1000 You invest $2000 in an account earning 3% interest compounded continuously. How long will it be until you have $2500? A: 2500 = 2000 e (. 03 t) S 2 C 13 Jeopardy Review t = 7. 44 years

Solving Logarithmic Equations 200 2 log 24 – log 22 = A: log 28 = 3 S 2 C 13 Jeopardy Review

Solving Logarithmic Equations 400 log 9 √ 81 A: 1 S 2 C 13 Jeopardy Review

Solving Logarithmic Equations 600 Solve for x. log 5 x = 2 A: 102 = 5 x S 2 C 13 Jeopardy Review x = 20

Solving Logarithmic Equations 800 Solve for x. ln 3 + ln x – ln 2 = 6 A: ln (3 x/2) = 6 S 2 C 13 Jeopardy Review x = 268. 953

Solving Logarithmic Equations 1000 ln x + ln (x + 3) = 2 A: ln (x 2 + 3 x) = 2 S 2 C 13 Jeopardy Review x = 1. 6, using quadratic formula

Solving Exponential Equations 200 x 2 = 49 A: 7 or -7 S 2 C 13 Jeopardy Review

Solving Exponential Equations 400 4 x⅔ = 20 A: x = 11. 18 S 2 C 13 Jeopardy Review

Solving Exponential Equations 600 3 x – 4 = 6 A: x = 2. 096 S 2 C 13 Jeopardy Review

Solving Exponential Equations 800 4√m 3 A: m = 16 S 2 C 13 Jeopardy Review + 2 = 10

Solving Exponential Equations 1000 e 4 x = 10 A: 4 x = ln 10 S 2 C 13 Jeopardy Review x =. 576