Solve showing work.

- Linear, Exponential, and Quadratic Regression

- Logarithms and Graphing Logarithms

Solve by graphing. 24. log x = log (2x2 - 1) 25. -7 + 5logs (2x - 7) =-17 Determine the best function to model the data below and find the equation. 26. f(x) 27. 28 f(x) 1.6 0 56 3.2 -1.5 2 6.4 2 -2 2 50 3 12.8 3 -2.5 3 35 25.6 -3 12 Find f(6) = Find f(6) = Find f(6) = 29. Two types of cars have different projected depreciation values. Their changing values are modeled as shown. Find the average rate of change of the value of each car over the 10-year period. Which car's value decreases more quickly over the interval [0, 10]? Car 1 Car 2 f(x) = 40(0.90)' (thousands of dollars in x years) (10 9 84 Tho 6 8 16 12x Years Find the inverse of each of the following functions. 30. f(x) = log3(x+1) 31. g(x) = 7x+4 a) g (x ) = 3x - 1 a) g(x) = log7(x) - 4 b) g(x) = log3(x) - 1 b) g(x) = log7(4x) c) g(x) = 3x - 1 c) g(x) = log4(x) + 7 ( 2 21) d) g(x) = 2x d) g(x) = 4log7(x) 32. The graph shows the function f(x) = 6(2)*. What is the value of the inverse function, f , at x = 3? ( - 1.3 )Find the intercepts and asymptotes. 1. y = logs (x + 1) 2. y = 2(2) * +1 + 3 Asymptote: Asymptote: y-intercept: y-intercept: 3. A $12,500 car depreciates 9% each year. How much will the car be worth after 5 years? 4. A baseball card bought for $50 increases 3% in value each year. How much will the card be worth after 7 years? 5. If you invest $1000 at an annual interest rate of 4.8% compounded monthly, how much will you have after 2 years? 6. If you invest $3500 compounded quarterly at a rate of 4%, how much will it be worth after 15 years? 7. For each of the following, determine if the function represents growth or decay. Then find the growth/decay rate (%). a. f(x) = 800(0.945)* b. g(x) = 1500(1.23) * 8. The population of turtles in a lake is estimated at 1,000. The population is projected to increase 12% per year. Write an exponential function you can use to identify the: a. monthly growth rate b. quarterly growth rate Write an exponential equation whose graph passes through (1, 6) and (2,15). Which of the following points are also on the exponential equations? (0, -9) (0, 2.4) (3, 37.5) (3, 24) Describe the transformations and determine the appropriate asymptote for each of the following: 10. f(x) =3* and g(x) = = -2(3)*+ 4 11. h(x) = logs(x) and j(x) = logs(x - 1) + 3 Evaluate (Round to the nearest ten thousandth place when appropriate): 12. log2 64 13. log2 1.7 14. log 1.65 15. log -5 16. In(1) Convert the following from logarithmic form to exponential or vice versa. 17. log4(64) = 3 18. log(0.1) = -1 19. 34 = 81 20. 25 = 32 Solve (Round to the nearest thousandth place when appropriate). 21. 7x - 3 = 25 22. log2 4x = 5 23. 43x - 1 = (1/2)*+5