Exponential and Logarithmic Functions Review

Algebra 2/Trigonometry UNIT 6: Exponential & Logarithmic Functions - REVIEW NC: Non-Calculator Name: Date: C: Calculator Permitted Section 1: Given each function, provide an example of a graph that will match each description (NC). Then, graph only the exponential equations (all f(x) equations). 1.) DESCRIPTION a) Horizontal shift LEFT 3 units f(x) = 3 ^ x b) Horizontal shift RIGHT 2 units f(x) = 3 ^ (x - 2) c) Vertical shift UP 4 units d) Vertical shift DOWN 5 units e) Reflection over the x-axis 1) Reflection over the y-axis f(x) = 3 ^ (- x) f(x) = - 3 ^ x f(x) = 3 ^ x - 5 g(x) = log(x) g ) + 4 g(x) = log(x + 3) 4(x) = 186(x) - 5 q(x) = log(x) g(x) - log(- x) Section 2: Rewrite each exponential equation in logarithmic form (NC). 2.) 5 ^ x = 625 3.) 10 ^ x = 1000 lc*g_{5} * 625 = x 4.) e ^ 3 = 20.085 ln(20085) = 3 5.) u ^ v = w logi loguw= V log(10c * 0 = x) Section each logarithmic equation in exponential form (NC). 6.) log_2(1/(it)) = - 3 2 ^ - 3 = 1/6 7.) In 143 = x 8.) log_4(64) = 3 4 ^ 3 = 64 9.) log(1/100) = - 2 10 ^ - 2 =\%00 Section 4: Evaluate (NC-#10-15. c-\# 16 - 18 Round to the nearest thousandths). e ^ x = 143 10.) log_4(4 ^ 2) = underline ? 11) Ine³ = 3 13.) 210855 14.) eln 12 12 16.) log_3(8) = underline underline boxed 8 boxed 3 underline boxed 8 17.) logs 12 = 1.544 12.) log(10 ^ 2) = 2 \ 15.) 10 ^ log(4) =\ 18.) log_2(7) = m - 7 radicals (NC). Section 5: Expand each logarithmic expression. Your answer may not contain any expressions or log(x ^ 3) + log(sqrt(y + 1)) + log(z ^ 2) 19.) 3 * log(x) + 1/2 * log(y + 1) - 2 * log(z) log((x ^ 3 * sqrt(y + 1))/(x ^ 2)) Section 6: Condense each logarithmic expression (NC). 20.) In ((y*pi*vx)/w) * Iny + ln(2) + ln(sqrt(x)) - ln(w) ln(y equiv sqrt x ) - ln(y) * 0 ln(y) + ln(z) + 1/2 * ln(x) - ln(w') 21.) 3 * log(x) + 2 * log(y) + 1/2 * log(z) tos( x * y ^ 2 * sqrt(2) 22.) 3 * ln(x) + 2 * ln(5) - ln(x + 2) * ln((265lambda ^ 3)/(x + 2)) For additional practice from each section on this review sheet - see the Unit 6 Additional Practice PDF (with answer key) posted on my website! f(x) = 3 ^ x + 4 f(x) = 3 ^ (x + 3) Algebra 2/Trigonometry UNIT 6: Exponential & Logarithmic Functions - REVIEW Name: Date: Section 7: Solving Exponential Equations (C). Round any irrational answers to the nearest hundredths. 23.) 3 ^ (x - 2) = 27 log(3) , 27=x-2 x=5 24.) e ^ (x + 5) = e ^ 7 (x + 5 = 7)/(x = 2) 25.) 4 ^ x = 42 boxed x = 2.7 boxed x=2.70 26.) 4(5 ^ (x + 2)) = 32 ln(xy * 8 = x + 2) x ^ 2 + 0, 71 27.) e ^ x = 18 M * 3 = x 28.) 3e ^ x = 24 ln(8) = x 5 ^ (x + 2) = 8 Section (C). Round any to the hundredths. sqrt(x) \approx 2.89 e ^ 2 = 8 e=x 30.) x = 2 35x+x=238 29.) log_4(x - 1) = 2 x = 17 31.) log(x) = 6 1000000 f * 0 ^ 6 = x 33.) log_3(x) + log_3(x - 8) = 2 ) 5 ^ 2 = x ^ 2 - 8x \\ x--8x-9 aligned 35.) 5x - 1 = x + 7 log_3(5x - 1) = log_3(x + 7) 32.) log_3(x + 5) = 5 \\ <4 34.) log_4(x) - log_4(x - 1) = 1/2 x ^ 2 - x - 2 4 ^ (1/2) = x ^ 2 - x (x - 2)(x - 1) 36.) log 6 (3x+14)^ (x = 2)/(- log_6(5)) = log_6(2x) 3x + 14 = 16x (9x + 14)/3 - 2x 7x = 19 Section 9: Application Problems (C). Simple Compound Interest: A = P * (1 + r/n) ^ (nt) Continuous Compound Interest: A = P * e ^ (rt) 37.) Emily plans to put her graduation money into an account and leave it there for 4 years while she goes to college. She receives $1,050 in graduation money to college that she puts into an account that earns 4.25%. How much money will be in Emily's account at the end of four years if it is compounded? $1243.45 a.) Quarterly? F1244.20 b) Monthly? $1244.57 Continuously? dot A =1054(1+ *0425 12 )^ 4i_{2} A-1050(0425 38.) The number of people infected by the flu in a particular region after t hours is given by: P(t) = 5e ^ (0.03t) where t >= 0 a.) Is this a growth or decay problem? growth (+,03) b.) What is the initial population of people infected by the flu? 5 people c.) What is the population of people infected by the flu after 12 hours? P(12) Se E = 24hrs P(24) = 5epsilon %2 03-12 8 people Il people d.) What is the population of people infected by the flu after 1 day? 39.) The population of mosquitoes after t days is given by: P(t) = 500e ^ (-0.055t) where t >= 0 055 (1) =1474 naquitoes 2-3 days P(3)= 50c C.055 (3) - 1424 mosquitoes a.) Is this a growth or decay problem? de ca b.) What is the initial population of mosquitoes? 500 rosquitoes c.) What is the population of mosquitoes after 1 day?) = 600 e d.) What is the population of mosquitoes after 72 hours? For additional practice from each section on this review sheet - see the Unit 6 Additional Practice PDF (with answer key) posted on my website! (y - 6)/(x - 2) 4 ^ 2 - x - 1 x approx7.39| 50 (1 + 425/4) ^ N+ x = 2, - K