1. An exponential function is a function with a constant base that is changed by x, a variable. Exponential functions are used to predict changes in murder rates, bacteria growth even investments. This function can also be used in predicting rate of decay such as automobile value and radioactive half-life. 2. The natural exponential function, f(x) = ex, has a known base constant.
Unlike other exponential functions where the constant, a, can be any real number, e is always 2.718. A good example of a natural exponential function is continuous compound interest. 3. Evaluate 4-1.5 = 0.125 4. Using the formula S = C(1 + r)t If the inflation rate is 3%, how much will a will a house now worth $510,000 be worth in five years? S = $510,000 ( 1 + .03 )5 S = $510,000 x 1.035 S = $591,229.78 5. Write 6 = log2 64 in its equivalent exponential form. y = loga x 6 = log2 64 x = ay 64 = 26 6. Write 8y = 300 in its equivalent logarithmic form. y = bx

300 = 8y

logb (y) = x

log8 (300) = y

7. Using the formula: f(x) = 0.48 In (x+1) + 27 a. Evaluate f(0) and f(100). Interpret the result. f(0) = 0.48in (1) + 27 = 27 says the barometric pressure at the eye is 27 f(100) = 0.48 (101) + 27 = 29.215 says the barometric pressure 100 miles from the eye is approximately 29.2 b. At what distance from the eye of the hurricane is the air pressure 28 inches of mercury? 0.48In(x+1) + 27 = 28 0.48In(x=1) = 1 In(x+1) = 1/0.48 ≈ 2.083 ein(x+1) ≈ e2.08 x + 1 ≈ e2.08 x ≈ e2.08 – 1 x ≈ 7
8. Describe the quotient rule for logarithms and give an example. The quotient