Algebra 2 - Classwork April 25, Review

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1 Name: ID: A Algebra 2 - Classwork April 25, Review Graph the exponential function.. y 4 x 2. Find the annual percent increase or decrease that y 0.5(2.) x models. a. 20% increase c. 5% decrease b. 5% increase d. 65% decrease. An initial population of 820 quail increases at an annual rate of 2%. Write an exponential function to model the quail population. What will the approximate population be after years? a. f(x) 820(.2) x ; 526 c. f(x) ( ) x ; 6,708,494 b. f(x) 820(2) x ; 9,976,940 d. f(x) 820(0.2) x ; 526

2 Algebra 2 - Classwork April 25, Review Page: 2 Graph the function. 4. y 8 x Ê ˆ Á 2

3 Algebra 2 - Classwork April 25, Review Page: 5. y 2 x Ê ˆ Á 8

4 Algebra 2 - Classwork April 25, Review Page: 4 6. y 5 x Ê ˆ Á 4 2 4

5 Algebra 2 - Classwork April 25, Review Page: 5 7. y 4 x 4 Ê ˆ Á 2 8. The half-life of a certain radioactive material is 2 days. An initial amount of the material has a mass of 6 kg. Write an exponential function that models the decay of this material. Find how much radioactive material remains after 5 days. Round your answer to the nearest thousandth. Ê a. y 6 ˆ Á 2 2x Ê ˆ 2 x ; 0 kg c. y 2 Á 6 ; kg Ê b. y 6 ˆ 2 x Á 2 ; kg d. y 2 Ê ˆ Á 6 2 x ; 0.99 kg 9. Use the graph of y e x to evaluate e.7 to four decimal places. a b c d

6 Algebra 2 - Classwork April 25, Review Page: 6 0. Suppose you invest $600 at an annual interest rate of 4.6% compounded continuously. How much will you have in the account after 4 years? a. $ b. $6,70.28 c. $0,8.07 d. $,92.2. How much money invested at 5% compounded continuously for years will yield $820? a. $ b. $88.84 c. $780.0 d. $ You open a savings account and deposit $,000. After year of earning continuously compounded interest, your balance is $,08.6. After 2 years, the balance is $, Assuming you make no deposits or withdrawals, find the equation for the best-fitting exponential function to represent the balance of the account after x years. How much money will be in the account after 0 years? a. A 000 e.8, $6, c. A 000 e 0.08t, $,97.22 b. A 000 e 0.08t, $,00.20 d. A 000 e.8 * t, $,00.20 Write the equation in logarithmic form a. log c. log 2 5 b. log d. log a. log c. log b. log d. log Write the equation in exponential form. 5. log a c b d log (a b) c 6 a. (a b) 6 c c. c 6 (a b) b. 6 (a b) c d. (a b) c 6 6

7 Algebra 2 - Classwork April 25, Review Page: 7 Evaluate the logarithm. 7. log a. b. 5 c. 4 d log 24 a. 5 b. 5 c. 4 d. 9. log 0.0 a. 0 b. 2 c. 2 d The table shows the location and magnitude of some notable earthquakes. How many times more energy was released by the earthquake in Mexico than by the earthquake in Afghanistan? Use the given equation for comparing earthquake intensity level and magnitude. log I I 2 M M 2 Earthquake Location Date Richter Scale Measure Italy October, El Salvador February, Afghanistan May 0, Mexico January 22, Peru June 2, a. about 0.70 times as much energy c. about 7 times as much energy b. about 2.6 times as much energy d. about 5.0 times as much energy 2. The ph of a liquid is a measure of how acidic or basic it is. The concentration of hydrogen ions in a liquid is È È labeled H ÎÍ. Use the formula ph = log H ÎÍ to find the ph level, to the nearest tenth, of a liquid with [H+ ] about a..8 b..8 c. 2.2 d..0 Solve the exponential equation x a. 2 b. 4 c. 7 2 d x 8 a. 4 b. 8 c. 8 d. 2 7

8 Algebra 2 - Classwork April 25, Review Page: x 2 50 a b c d Solve 5 2x 6. Round to the nearest ten-thousandth. a b c d..909 Solve the logarithmic equation. Round to the nearest ten-thousandth if necessary. 26. log2x 4 a b. 5 c d Solve log(4x 0). a. 7 4 b c. 250 d Simplify ln e. a. b. e c. e d. Use natural logarithms to solve the equation. Round to the nearest thousandth e 4x 2 a b c d e x 4 a b c d The sales of lawn mowers t years after a particular model is introduced is given by the function y 5500 ln(9t 4), where y is the number of mowers sold. How many mowers will be sold 4 years after a model is introduced? Round the answer to the nearest whole number. a. 20,289 mowers c. 8,8 mowers b. 4,709 mowers d. 9,7 mowers 2. Without graphing, determine whether the function y ( 5.2) x represents exponential growth or exponential decay. Ê. Without graphing, determine whether the function y 7 2 ˆ Á decay. x represents exponential growth or exponential 4. In a particular region of a national park, there are currently 0 deer, and the population is increasing at an annual rate of %. a. Write an exponential function to model the deer population. b. Explain what each value in the model represents. c. Predict the number of deer that will be in the region after five years. Show your work. 8