TEST TOMORROW 3/1/ NON-CALCULATOR MULTIPLE CHOICE 15-FREE RESPONSE QUESTIONS Unit 2 review

Unit 2 test review 1) y = 3 x 2. y = -2(0.75) x Domain: all real #’sDomain: all real #’s Range: y > 0Range: y < 0

3) $ ) $ ) a. $16, b.$16,487.21

6) 7) 8) 9) 310) 411) 2/3

12) 13) 14) 15) 1

16) ) ) ) 2520) ) 4.266…22)40 23) ) ) )0.6065

27) a years ( 1 year & 7 months) b years

Unit 2 overview Logarithm  Evaluate, Properties, and solve  Natural logs Exponential  Growth and decay graphs  Growth and decay word problems (savings)

Unit 2- exponential functions Standard Form: y = ab x a = Y - INTERCEPT b = 0 < b < 1, DECAY b > 1, Growth Sketch a graph of each equation y = 3 x y = 2(0.75) x Domain: ALL REAL# Range: y > 0

Growth or Decay??? y = 8 x y = 4 · 9 x y = 0.65 x y = 3 · 1.5 x y = 0.1 · 0.9 x y = 0.7 · 3.3 x

Unit 2- exponential word problems Growth/Decay$ compounded Continuously $ compounded n, number of times

$200 principal, 4% compounded annually for 5 years $1000 principal, 3.6% compounded monthly for 10 years $3000 investment, 8% loss each year for 3 years

Find the balance in each account. You deposit $2500 in a savings account with 3% interest compounded annually. What is the balance in the account after 6 years? You deposit $750 in an account with 7% interest compounded semiannually. What is the balance in the account after 4 years? You deposit $520 in an account with 4% interest compounded monthly. What is the balance in the account after 5 years?

Unit 2 - LOGARITHMS Logarithms: log b a = x → b x =a log a = x → 10 x =a ln a = x → e x =a

Unit 2 – Solving exponential Solving Exponential Equations Get the Base & exponent alone. Then write in LOG form, Solve for the variable

Unit 2 – log properties Use log properties to combine logs ADD = Multiply, Sub =Divide, # in front goes as Exponent Write each expression as a single logarithm. 17. log 8 + log log x + 4 log x 19. log 4 + log 2  log 5

Unit 2 – solving log equations Use properties to combine into single log Then write in EXPONENTIAL form, then solve for the variable. 20. log 3x − log 5 = log x − log 3 = log 8 − log 2x = − ln x  ln 4 = 7

Logarithms Logarithms are used to solve for the exponent. (it gets the exponent alone) Write each in log form: 1) 100 = ) 3 4 = 81 Write each in exponential form: 125 = 5 3 e 1.61 = 5

Properties of logs Write each as a single log

Solve

EXPONENTIAL Expo. Growth and decay Ending amount Initial amount Rate(decimal) Time

Exponential growth/decay If you invest $1000 in a savings account that pays 5% annual interest. How much money will you have after six years?  You buy a new computer for $800. it is expected to depreciated 12% each year. How long will it take for the computer to be worth $500? $ years