Assume that Sophia and John have the following value function over exam scores:v(x) = x/2 for gainsv(x) = 2x for lossesBoth of them use the expected exam score as their reference point.1. Sophia expects to score 75 out of 100 on her upcoming midterm exam. What is her gain, in terms of value, if herfinal score is 93?2. John also expects to score 75 out of 100 on his upcoming midterm exam. What is his loss, in terms of value, ifhis final score is 67?3. If you use your expectation as a reference point, should you set high or low expectations for yourself?

To solve both a and b part first we have to evaluate wheather there is gain or loss. Gain or loss is…

Answered: Assume that Sophia and John have the…

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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1. Consider the functions f (x) =÷x – 1 and g(x) = x² – 4. (a) Graph each function by filling in the table below. f(x) %=D글x-1 g(x) = x - 4 -2 -1 -9- -4 -3 -2 -1 3 4 6. -2 1 -3 2. For the problems below, show your work and report your answers as ordered pairs. (b) Give the x- intercepts of the function g(x) = x² – 4. %3D (c) Give the y- intercept of the function f (x) = x- 1.
The U.S. population can be modeled by the function y=165.6x¹.345, where y is in thousands and x is the number of years after 1800. (a) What was the population in 1970, according to this model? (b) is the graph of this function concave up or concave down? What does this mean? (c) Use numerical or graphical methods to find when the model estimates the population was 94,150,000. (a) According to the model, the population in 1970 was thousands. (Round to the nearest integer as needed.)
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2. Lijah opened an account at Advantis Credit Union. The balance of her account after x years is represented by the function b(x) = 500(1.05)*. What annual interest rate is Lijah earning? а. b. After how many years did it take for Lijah's balance to double? Show all of your work.
differntiate question 3,4 and 5
25. (a) Determine whether y = 3. 7* is a linear, power, or exponential function (i.e, choose one column,and fill in the missing values in that column. Linear Function slope = Power Function coefficient = Exponential Function initial value = y-intercept = exponent = b = (b) Determine whether y = is a linear, power, or exponential function (i.e, choose one column,and fill in the missing values in that column. Exponential Function initial value Linear Function Power Function coefficient = slope = y-intercept = exponent = (c) Determine wheter y = 3- (r+10)-7x is a linear, power, or exponential function (i.e, choose one column,and fill in the missing values in that column. Linear Function slope = Power Function coefficient = Exponential Function initial value = y-intercept = exponent = b = (d) Determine wheter y = 12" · 997 is a linear, power, or exponential function (i.e, choose one column,and fill in the missing values in that column. Linear Function slope = Power Function coefficient =…
54. U.S. households with cable/satellite TV Suppose the rate of change of the percent P of U.S. households with cable/satellite TV can be modeled by dP 46.20 %3D dt t + 5 where t is the number of years past 1975. (a) Use integration and the data point for 2007 to find the function P(t) that models the percent of U.S. households with cable/satellite TV. (b) How well does the model from part (a) fit the data in the table? Explain. (c) If the model remains valid, use it to predict the percent of U.S. households with cable/satellite TV in 2020. Year Percent Year Percent 1980 22.6 2000 67.8 1985 46.2 2005 85.7 1990 59.0 2007 83.8 1995 65.7 2009 89.7 Source: Nielsen Media Research
Element X is a radioactive isotope such that its mass decreases by 20% every year. Ifan experiment starts out with 730 grams of Element X, write a function to representthe mass of the sample after t years, where the monthly rate of change can be foundfrom a constant in the function. Round all coefficients in the function to four decimalplaces. Also, determine the percentage rate of change per month, to the nearesthundredth of a percent.

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