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NAME_________________________________ PD___ Warm Ups: Exponential/Logarithmic Functions 6 WHERE AM I GOING? What are characteristics of graphs of exponential functions? What value does e represent? How can exponential functions be used in real-world problems? What is a logarithm? WHERE AM I NOW? How can you solve exponential and logarithmic equations? 6.1-1 Without graphing, determine whether each equation represents growth or decay: 1) y = 15(7)x 2) y = 1285(0.5)x Identify the horizontal asymptote of: 3) Y = (0.8)x 4) y = 3(0.25)x - 1 Write an exponential function for the graph that passes through the points (-1, 5) and (1/2, 40) 6.1-2 WRITE AN EXPONENTIAL MODEL FOR EACH OF THE FOLLOWING: 1) A car valued at $9000 depreciates at a rate of 15%. 2) The deer population of 2400 in an area increases by 11% each year. 3) The half-life of a radioactive substance is 5 days. The original amount of the substance is 48 mg. 6.2 1) Find the amount in a continuously compounded account where the principal is $2000 at an annual interest rate of 5% for 3 years. 2) How much must you deposit in an account paying 4.5% interest compounded monthly to have $4000 in five years? M. Murray 6.3: NO CALCULATOR: EVALUATE EACH LOGARITHM 1) log232 2) log (-100) 3) log 41 Write each equation in exponential form: 4) Log 0.01 = -2 5) log327 = 3 What is a logarithm? 6.5: PROPERTIES OF LOG EXPAND: 1) log2x3y 2) log abc2 Condense (simplify): 3) 4log x + log y – log z 4) log 1 – 2log x 6.6: SOLVE: 1) log (7x + 1) = log (x – 2) + 1 2) 4x-2 = 89 3) 2log x + log 4 = 2 4) 42x – 4 = 13 6.6 SOLVE: 1) 2 ln x + 3 ln 2 = 5 2) 4e(x-1) = 64 3) ln 4 – ln x = 10 4) e3x = 12