In Exercises 9-10, complete the table. 9. f(x) = x² - 2 X f(x) 10. g(t) t g(t) -2 2 3 |t-1| -5 -3 0 1 2 1 3 10
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- In Exercises 1–4, an object dropped from rest from the top of a tallbuilding falls y = 16t2 feet in the first t seconds. 1. Find the average speed during the first 3 seconds of fall.2. Find the average speed during the first 4 seconds of fall. 3. Find the speed of the object at t ! 3 seconds and confirm youranswer algebraically. 4. Find the speed of the object at t ! 4 seconds and confirm youranswer algebraically.In Exercises 15–22, calculate the approximation for the given function and interval. 15. R3, f(x)=7−x, [3,5]Use the models f(x) = 0.074x + 2.294 and g(x) = 2.577(1.017)x to solve this problem. a. World population in 1970 was 3.7 billion. Which function serves as a better model for this year? b. By one projection, world population is expected to reach 9.3 billion by 2050. Which function serves as a better model for this projection?
- . As a business student and a computer scientist, a research has been conducted and the problem has been modeled below, (a) Max s.t . Critically analyze and solve the problem algebraically, interpret your results and discuss vividly.In a learning theory project, psychologists discovered that f(t) = 0.8 / 1 + e-0.2t is a model for describing the proportion of correct responses, f(t), after t learning trials. Solve, a. Find the proportion of correct responses prior to learning trials taking place. b. Find the proportion of correct responses after 10 learning trials. c. What is the limiting size of f(t), the proportion of correct responses, as continued learning trials take place?General Electric models the time X in years that a new microwave will last using the following PDF f(x)= (3x2e(−x^3/8^3))/8^3, x>0 (a) Write out the CDF and quantile formulas. (b) What proportion of microwaves does GE anticipate will last at least 10 years? (c) What is the median length of time until failure for a new microwave?
- A study indicates that spending money on pollution control is effective up to a point but eventually becomes wasteful. Suppose it is known that when x million dollars is spent on controlling pollution, the percentage of pollution removed is given by P(x) = (100 √x) / (0.03x² + 9 )(i) At what rate is the percentage of pollution removal P (x) changing when 16 million dollars is spent? Is the percentage increasing or decreasing at this level of expenditure? (ii) For what values of x is P (x) increasing?(iii) For what values of x is P (x) decreasingHow do you solve this? The image says: In Exercises 1-6, evaluate the function when x = -4, 0, and 2. 1. f(x) = -x + 4 2. g(x) = 5x 3. h(x) = 7 - 2x 4. s(x) = 12 - 0.25x 5. t(x) = 6 + 3x - 2 6. u(x) = -2 - 2x + 7 In Exercises 7 - 9, evaluate the function when x = -2, 0, and 5. 7. f(x) = x - 3 8. g(x) = -2x 9. h(x) = 5 - 3x In Exercises 10 - 17 find the value of x so that the function has a given value. 10. b(x) = -3x + 1 ; b(x) = -20 11. r(x) = 4x - 3 ; r(x) = 33 12. m(x) = -3/5x - 4 ; m(x) = 2 13. w(x) = 5/6x - 3 ; w(x) = -18 14. f(x) = 6x ; f(x) = -24 15. g(x) = -10x ; g(x) = 15 16. f(x) = 3x - 5 ; f(x) = 4 17. h(x) 14 - 8x ; h(x) = -21. How do you find the linearization of f(x) at x = a? Illustrate with a concrete example
- A house is purchased for $140,000 in January 2004. A year later, the house next door is sold for $149,800. The two houses are of the same style and size and are in similar condition, so they should have equal value.Use the model v = 140e0.0676586485t, where t is the number of years after January 2004 and v is the value in thousands of dollars, to predict when the house would be worth $290,000.a). When do you think P, performance, increases most rapidly? b). Explain what happens to dp/ dt as t increases. c). If M is the maximum level of performance of which the learner is capable, explain what happens, both mathematically and in the context of learning, when M = P. dP/dt= k(M-P) k is a positive constantTrue or False? The function k(x)=3x/the square root of 5-x is guaranteed to have an absolute maximum and minimum on the interval (0,4).
