Pg. 259/245/68 HW Review Pg. 255#6, 14, 24, 28, 35, 51 Pg. 268#1, 3, 5 – 9 odd, 15 #58#59 ft/sec #60#61t = sec #62 V(t) = 36πt 3 #63V(5) = 14, cu in. #64 t = 5.10 sec.#38 #39 Graph#40r=3.84; h=7.67; S= #41 #42Graph; 20 < L < 45 #43 L = 30; P = 120#69t ≥ 3.63 sec

5.1 Exponential Functions Definitions Let a be a positive real number other than 1. The function f(x) = a x, whose domain is the set of all real numbers, is the exponential function with base a. If a > 1, the function will be increasing. If 0 < a < 1, the function will be decreasing. Without an transitions or reflections… D: (-∞,∞) R: (0,∞) If f(x) = ma (x + h) + k – A vertical stretch of m – A horizontal shift of h – A vertical shift of k

5.1 Exponential Functions Graph the following functions:The Natural Function The natural exponential function is the function f(x) = e x where e = the irrational number 2.718… The population equation is: A = P(1 ± r) t where + is exponential growth and – is exponential decay.

5.1 Exponential Functions Population The population of town P is 123,000 and is decreasing at the rate of 2.375% each year. Find an algebraic representation for P as a function of time. Determine when the population will be 50,000. Half-Life Suppose the half-life of a certain radioactive substance is 20 days and there are 5g present initially. Draw a complete graph of an algebraic representation of this problem situation and find when there will be less than 1g of the substance remaining.