Unit 3 Test Review Answer Key PDF

Unit 3 Test Review Key Name ___________________________________________________ Exponential, Logistic, &...

Unit 3 Test Review Key Name ___________________________________________________ Exponential, Logistic, & Date __________________________________ Period _________ Logarithmic Functions Calculator Inactive Use the properties of exponents to expand: 𝑥𝑥 3 𝑦𝑦 √𝑥𝑥𝑦𝑦 1. log 3 3𝑧𝑧 = 1093X3 + logzy-logy3-1093z 2. log 8 3 = 210yXy - 10983 = 310gzX + logzy - 1 + 10937 = [loggX + +loggy -10983 Solve: 3. 3log 2 𝑥𝑥 + 1 = 7 4. log √10 = 𝑥𝑥 3 1 5. ln 𝑒𝑒 7 = Ine" = - 7 C 31092X 6 = 10g , 103 = x log2 X In = 2 10* = 10137x = t or x= 24 => X = 4 6. Afghanistan suffered two major earthquakes in 1998. The first had a magnitude of R=6.1 and the 𝑎𝑎 second had a magnitude of R = 6.9. Use log 𝑇𝑇 + 𝐵𝐵 to find how many times more powerful the second quake was. Assume that the values of B and T are equal for both earthquakes. Rc - R , = log(4) + B - [log( < ) + B] 6 9. - b. 1 = 10gaz -109T + & 110g9 - , -T B) + 0 8 = 10gaz-1099 10086 310 times stronger. & , = 0 8. = 10994a, =. 7. Write the exponential function that satisfies the conditions: Initial population = 67000, decreasing at a rate of 1.67% per year. P(t) = 67000 0167)t(1 - 0. p(t) = 67000(0 9833)t. 8. Write the exponential function that satisfies the conditions: Initial population = 67000, increasing at a rate of 1.67% per year. P(t) = 67000 (1 + 0 0107) t. P(t) = 67 , 000 (1 0167) , + 3 9. Rewrite as an exponential expression: log 3 8 = 𝑥𝑥. 34 = 5 10. Condense and simplify: 2 ln 𝑥𝑥𝑦𝑦 2 − 3 ln 𝑦𝑦. © 2020 Jean Adams All rights reserved. In (xy2)" - Inys = In X In xh  Calculator Active: x All It Foo x((n4 (n7) Solve: If there are any extraneous solutions, tell why they are extraneous. 31n4 X= xit - = ↑ - In 4x +3 In =747𝑥𝑥 log[(x + 2)(x 1)] 104 - = 2 11. 4𝑥𝑥+3= 31n4 - 12. log(𝑥𝑥 + 2) + log(𝑥𝑥 − 1) = 4 (x + 3)(n4 Xin7 X = x x + 2x 2 10000 = In4-In7 - - = x(n7 X- + x 10002 = 0 Z x(n4 3(ny - + = 31n4 - x \n4 -xIn7 = - 31n4 or X= in7-iny x i = t #00090 2(1) so it's extraneous In 61 = In ex e - 44 50 14. 1000𝑒𝑒 =750 = −4𝑥𝑥= 075 13.. 4+𝑒𝑒 2𝑥𝑥 = 11 - 4x = In 0 075. X= - +10. 75 15. The number P of students infected with the flu at Olympia High School 𝑡𝑡 days after exposure 300 is modeled by: 𝑃𝑃(𝑡𝑡) = 1+𝑒𝑒 4−𝑡𝑡 a. What was the initial number of students infected with the flu? P(a) = 5 39. 5 students b. When will 100 students be infected? t= 4 In 2 ↑ - e t 1 + 3 o = t += 3 307 e4 - = 2 , 4-t = In2 on the 4th day c. What would be the maximum number of students infected? 300 16. The pH of sea water is 7.6 and the pH of milk of magnesia is 10.5. pH = -log[Ht] a. What are the hydrogen ion concentrations of each? log [H ] 10 5 milko + 7,6 - TH ] 10. = + : - sea water = a [H +] =2 512x108 mol/ ~ 3 162x10 "moly - = 10.. b. How many times greater is the hydrogen-ion concentration of sea water than of milk of magnesia? sea water milk of magnesia : = 1029794. 33 times © 2020 Jean Adams All rights reserved.  17. What will the balance be after 10 years if $1500 is invested at 1.5% interest compounded continuously? A= Pert 0 015. (10) A = 1500 e = $1742 75 , 18. The population of a community (in thousands) is 𝑃𝑃 = 224𝑒𝑒 0.0142𝑡𝑡 where t = 0 represents the year 2000. Predict the population in the year 2020. > += 20 - 0142(201 22490 thousand. P(20) = = 297 569. 297569 2 −5 19. Graph the function and analyze: 𝑒𝑒 𝑥𝑥 − 2 = 𝑓𝑓(𝑥𝑥) f(x) i (0 , 9) Range: __________________ Domain: ___________________ zao [0 ) Increasing on interval: __________________________ , ( 0 , 0] Decreasing on interval: ________________________ - - 2. 386" 2 , 386 · - VA: ______________ none HA: _________________ none - 1 9934 f(p) 2. = e - 20. The graph of an exponential function ℎ(𝑥𝑥) = 𝑎𝑎 ∙ 𝑏𝑏 𝑥𝑥 + 𝑐𝑐 is shown at right. a. Find the values of a, b and c. y = 3 HA : y = 3 = c= 3 a = - 1 (+ , 1) (0 , 2) (0 2) b+ = = 2= a 3 [. b > , = - = A (2 / 1) 54 3 (1 , 1) =) = - + 3 1 = 1 + 3 - b. Write the equation for the function. h(x) = = (t)* + 3 c. Is this exponential growth or decay? Explain. negative decay and Olb < / blc acO d. State the end behavior. lim h(x) = - x X+ - Y lim © 2020 Jean Adams All rights reserved. h(x) = 3 X- x 21. Due to advances in medicine and higher standards of living, life expectancy has been increasing in most developed countries since the beginning of the 20th century. The table below shows the average life expectancies, in years, of Americans from 1900–2010. Using t = 1 for 1900, t = 2 for 1910, and so on, create a scatter plot for the data on your calculator Year 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 Life 12345678910 11 12 Expectancy 47.3 50 54.1 59.7 62.9 68.2 69.7 70.8 73.7 75.4 76.8 78.7 (Years) (a) Based on your scatter plot, what type of function could be used to model the data? logistic (b) Perform an appropriate regression and write the equation of your function L in terms of t. Round all the coefficients to the nearest hundredth. 25 83. ((t) = 1 + 1 01e - 0. 13t. (c) Is your function a good fit? Justify your answer. It is a good fit because all the data points are very dose (d) Use your function to find the life expectancy in 2024 to the curve 2024 => t = 13 4 - even though the logarithmic function is a very good fit , the logistic growth function seems to line up better mth our data points >