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The function f is given by f(x) = 1000^x. If f(x) = 10, what is the value of x?

A) 1/3

The table gives value of an arithmetic sequence an for selected values of n. Which of the following linear functions is constructed from the initial value a0 (with n = 0) and common difference of the sequence?

A) 70 + 5x

The graphs show the residual plots resulting for cubic, quadratic, and linear regressions calculated on the same data set. Based on the plots, which of the following statements is best supported by the results?

A) The cubic model should be used.

The function h is given by h(x) = a * b^-x, where a < 0 and b > 1. Which of the following describes h and its graph in the xy-plane?

A) h is increasing, and the graph of h is concave down.

A certain hobby shop wants to attract customers on slow sales days by offering a new discount. The shop offers a 1.5% discount on Wednesdays with an added bonus for repeat customers. For customers who make purchases on succesive Wednesdays, their discount is doubled from the previous Wednesday yap yap yap

C) 8

The table gives five ordered pairs (x,y). Which of the following is true about the nature of the data?

C) A common ratio of y-values can be found as 1.25 after subtracting 7 from each y-value.

The first table gives selected coordinate pairs (x,y) that are a part of a larger data set. Using the five data points, three regressions were calculated, and the resulting linear, quadratic, and exponential equations are provided in the second table. It is know that the resulting linear, quadratic, and exponential regressions fit these five data points well. Which of the following additional pieces of information could help select a single best model?

C) Knowing that when the x-values are negative, the corresponding y-values are always between 0 and 1.

Terms in a sequence are given by sn = 4n + 7, for - 0,1,2,3, ... Which of the following describes the sequence?

C) The sequence is arithmetic with an initial value of 7 and a common difference of 4.

The tables give values of the functions f and g for selected values of x. What is the value of g^-1(f(2)) ?

D) 10

The number of bacteria in a dish is 1150 at time t = 0 hours. The number of bacteria in the dish doubles every 3 hours. If the function B gives the number of bacteria in the dish at time t hours for t => 0, which of the following could define B(t) ?

D) 1150 * 2^(t/3)

The graphs of y = f(x) and y = g(x) are given. What is the value of f(f(g(1)))?

D) 4

The first term in a geometric sequence is g1 = 5. For n=> 2, the terms of the geometric sequence are give by gn = 3 * g(n-1). For which of the following functions is gn = f(n) for positive integers values of n?

D) 5 * 3^(n-1)

The function f is given by f(x) = x + 2. If f^-1(n) = 4, what is the value of n?

D) 6

The fourth term of a geometric sequence is 7, the fifth term is 28/3, and the kth term is 7168/243. The solution to which of the following equations gives the value of k?

D) 7(4/3)^(x-4) = 7168/243

The ball is dropped for a heigh of 10 feet. The ball repeatedly bounces , and the maximum height of the ball after each bounce is 20% less than the previous maximum height. Which of the following arguments is correct regarding a sequence that can be used to model the successive maximum heights, in feet?

D) A geometric sequence is appropriate because each successive height would be found by multiplying the previous height by 0.8.

The graph of the function f is given. If g is the function given by g(x) = 2x, which of the following is the graph of the composite function y = f(g(x)) ?

D) The graph that is short but tall

A drop of water hits the surface of a lake and forms concentric circular ripples. The radius, in inches, of the circle enclosed by the outer ripple increases as a function of time t, in minutes, and is modeled by the function r given by r(t) = 25 sqroot 2t + 1. Which of the following gives the area of the circle enclosed by the outer ripple, in square inches, as a function of time t, in minutes?

B) 1250piet + 625pie

The table gives the population, in millions, of a certain region for selected years. An exponential regression of the form f(x) - a * b^x is calculated for the five data points, where x = 4 represents 2004 and x = 8 represents 2008. Based on the model f to predict the future population, in which year will the population first reach 35 million?

B) 2030

The function g is given by g(x) = 4 * 2^(3+x) . The function g can also be expressed as which of the following?

B) 32 * 2^x

The first term of a geometric sequence is 2/3. The next three terms are 1/2, 3/8, and 9/32. What is the tenth term of the sequence?

B) 6,561/131,072

The table gives five coordinate pairs (x,y). The function y = f(x) is a model based on a linear regression of the five pairs. The function y = g(x) is a model based on an exponential regression y = ab^x of the five pairs. Because of the limited number of data points for the residual plots, it is difficult to determine if the residuals show a pattern. As a result, both models f and g are being considered. The value k represents the sum of the absolute values of errors (residuals) of the linear model f. The value p represents the sum of the absolute values of the errors (residuals) of the exponential model g. If the selection of an appropriate model is based on the errors (residuals), which of the following is true?

B) Because k > p, the exponential model is preferred.

The graph of the function y = f(x) is given. Which of the following is the graph of y = f^-1(x)?

B) The one that starts at -2 and goes up to the 1st quadrant

The function f is given by f(x) = k + a * b^x , where a < 0, b > 1, and k is a real number. Which of the following is true?

B) lim f(x) as x -> negative infinity = k

In the xy-plane, the graphs of the linear function L and the exponential function E both pass through the points (0,2) and (1,6). The function f is given by f(x) = L(x) - E (x). What is the maximum value of f?

C) 0.540