1. Fill in the blanks with the appropriate term or expression. (a) f(x) = at is the exponential function with base where a > and a * (b) The logarithmic function with base a, denoted log, is defined by: loga (T) =y when a > and a # (c) loga = 0 and log. ( = 1 (d) log. = a- = x (e) In(x) is called the logarithm and is the logarithm with base 2. Give the domain of each function and state whether or not the function is increasing or decreasing on its domain. (a) f(x) = ex (b) g(z) = (c) h(x) = In(x) (d) F(x) = 10g2(x)3. Let a and y be real positive numbers, and let c be any real number. Determine whether the following statement is true or false. (a) True or false? In(r +y) = In(x) + In(y) In(x) (b) True or false? In(x - y) = In(y) (c) True or false? In(ry) = In(x) In(y) (d) True or false? In(ry) = In(x) + In(y) (e) True or false? In(x) - In(y) = In (f) True or false? In(xc) = cel (g) True or false? In(rc) = cln(x) (h) True or false? x = In(cr)4. The following function n(t) models the number of bacteria at time t where t is in hours. n(t) = 50e1.04t (a) What is the initial population of the bacteria? (b) True or false? After one hour, the initial population of the bacteria will have more than doubled. 5. (Bonus!) Let a > 1. Justify that log. (r) and at are inverses of each other. You can use that log. (I) and at are one-to-one without justification.6. [-16 Points} DETAILS SPRECALC7 4.2.027.Ml. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Animal populations are not capable of unrestricted growth because of limited habitat and food supplies. Under such conditions the population follows a logistic growth model: 0' Pt = (l 1+ke":E where c, d, and k are positive constants. For a certain fish population in a small pond d = 1200, k = 11, c = 0.2, and t is measured in years. The sh were introduced into the pond at time t = O. (a) How many sh were originally put in the pond? (b) Find the population after 10, 20, and 30 years. (Round your answers to the nearest whole number.) (c) Evaluate P(t) for large values oft. What value does the population approach as t ~ 00? m = E Does the graph shown confirm your calculations? P 1200 1000 800 600 400 200 10 20 30 40 O Yes O No12. [I1 Points] DETAILS SPRECALCT 4.3.056. MY NOTES ASK YOUR TEACHER | PRACTICE ANOTHER Find the function of the form y = loga(x) whose graph is given. y