A car was valued at $29,000 in the year 1990. The value depreciated to $15,000 by the year 2001. A) What was the annual rate of change between 1990 and 2001? r = Round the rate of decrease to 4 decimal places. B) What is the correct answer to part A written in percentage form? r = %. C) Assume that the car value continues to drop by the same percentage. What will the value be in the year 2005 ? value = $ Round to the nearest 50 dollars. Find an equation for the graph sketched below 8+ 7- 6 5 4 3 -5-4-3-2 2 3 4 -1 -2 -3- -4 -5 -6 f(x) = -7 -8- The graph below shows a transformation of y = 2 5- 4 -5-4-3-2X 3 2 1 1 2 3 4 5 -2 -3 Write an equation for the graph above. y= Express the equation in logarithmic form: (a) e = 4 is equivalent to In A = B. Then A=4 and B = x (b) e C = and D= = is equivalent to In CD. Then d b Match each equation with a graph above e 10% a. red b. green In(x) c. blue log(x) d. black B K Match each equation with a graph above: a. red (R) In(x) b. black (K) 10% c. blue (B) log(x) d. green (G) Match the formula of the logarithmic function to its graph. Graphs of Logarithmic Functions 5+ 4 Formulas for the Graphs a. f(x) = log(x) 3 2 1 -5-4-3-2-1 1 2 3 -1 -2 -3- --4- -5 5+ 4 3 2 1 -5-4-3-2-1 23 -1 -2 -3 -4 -5+ 5 4 3- 2- 1 -5-4-3-2-1 -1 -2 -3 -4 -5+ b. f(x) = -log(x) c. f(x) = log(x) d. f(x) = log(x) Write an expression, of the type A log(x + B) or A log(-(x+B)), for the transformed logarithmic function shown below: 6+- 5 4 3- 2 + 6 5 4 3 -x 3+ -4 -5 -6 f(x) = Hint: Use the vertical asymptote to find B. To solve for A, use a point on the graph and substitute the coordinates into: y = A log(x + B) or y = A log(-(x+B)), as appropriate. Match the formula of the logarithmic function to its graph. Graphs of Logarithmic Functions 5 4 3 2 1 -5-4-3-2-1 1 2 3 4 5 -1 -2 -3 -4- -5+ 5+ Formulas for the Graphs a. f(x) = -log3(x) b. f(x) = log(x) c. f(x) = log(x) d. f(x) = log(x) 4 3 2 1 -5-4-3-2-1 1 2 3 4 5 -1 WN -2- -3- -4 -5 5 4 3 2 1 -5-4-3-2-1 1 2 3 4 5 -1 -2- -3- -4- -5 O Match the formula of the logarithmic function to its graph. Graphs of Logarithmic Functions 5+ 4 3 2 1 Formulas for the Graphs a. f(x) = -log3(x) b. f(x) = log(x) c. f(x) = -log(x) d. f(x) = log(x) -5-4-3-2-1 /1 2 3 4 -1 -2-- -3- -4 -5+ 5- 4- 3 2 1 -5-4-3-2-1 1234 -1 -2- -3 --4-- -5-4-3-2-1 -5+ 5+ 4 3 2 1+ 1 2 3 4 -1 -2- -3 -4 -5-