2. Circle the function if it is exponential, or if it is a transformation of an exponential function: (g) f(x)=3-² (a) f(x) = 2²-3 (b) f(x) = 30.2 (c) f(x)=e³ (d) f(x) = -5² (e) f(x) = e (f) f(x) = x5 (h) f(x) =

Find the exponential function f(x) = a whose graph is given. f(x) = y 3 2 (-1,) -2 -1 1/2

A national census bureau predicts that a certain population will increase from 35.3 million in 2000 to 64.3 million in 2060. Complete parts (a) through (c) below. (a) Find an exponential function of the form f(t) = y₁b¹ for these data, in which t= 0 corresponds to 2000 and f(t) is in millions. f(t) (Use integers or decimals for any numbers in the expression. Round to four decimal places as needed.) (b) What is the projected population in 2030? In 2040? = In 2030, the population is projected to be (Round to one decimal place as needed.) million. million. In 2040, the population is projected to be (Round to one decimal place as needed.) (c) By experimenting with different values of t (or by using a graphing calculator to solve an appropriate equation), estimate the first full year in which the population will exceed 56 million. The first full year in which the population will exceed 56 million is

1. Consider the functions f (x) = log2x and g (x) = -2 log2 (x-3) + 4. a. Identify the domain and range for each function. b. Explain how the graph g(x) can be described as transformations of f(x).