Evaluating a Step Function In Exercises 27-30, evaluate the function for the given values.
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- High School Graduates The following table shows the number, in millions, graduating from high school in the United States in the given year. Year Number graduating in millions 1985 2.83 1987 2.65 1989 2.47 1991 2.29 a. By calculating difference, show that these data can be modeled using a linear function. b. What is the slope for the linear function modeling high school graduations? Explain in practical terms the meaning of the slope. c. Find a formula for a linear function that models these data. d. Express, using functional notation, the number graduating from high school in 1994, and then use your formula from part c to calculate that value.arrow_forwardThe productivity of workers at a shoe factory (in pairs of shoes per hour) can be modeled using the function p(h) = -2h + 5, where h is the number of hours. If a worker must create at least 3 pairs of shoes per hour for the company to be profitable, how long should the worker's shift be? O 5 O 6 07 O 8 O Sarrow_forwardthe number of commercial airline boarding on domestic flights increased steadily during the 1990s as shown in the table below. Let f(t) be number of commercial airline boardings on domestic flight (in millions) for the year that is t years since 1990. complete parts (a) thought (d) below. Number of Commercial Airlines Boardings on Domestic Flight Year Number of Boardings(million) 1991 452 1995 547 1997 599 1999 635 2000 666 a. what variable should be represented by the axes? what units should be displayed for the axes? what scaling should be used for the axes? b. find an equation of f. does your model fit the data well? c. use the model f to estimate the number of boarding in 2001. the actual number was 622 million. what is the error in your estimate? ( the error is the different between the estimated value and the actual value) d. the number of boarding in 2001 was low due to the terroist attacks on september 11,2001 by making…arrow_forward
- Abortions The number of abortions in the UnitedStates per 1000 women aged 15–44 can be modeledby the function y = -0.026x2 + 0.951x + 18.161,where x is the number of years after 1970 and y ismeasured in thousands.a. In what year does this model indicate the numberwas a maximum?b. What was the maximum number of abortions inthis year if this model is accurate?c. For what values of x can we be sure that this modelno longer applies?arrow_forwardEvaluate the function.arrow_forwardThe function provided estimates the average monthly temperature of a northern Alberta community, where 7 is the temperature in degrees Celcius and x is the month of the year such that the entire month of January has elapsed at x-1, the entire month of February has elapsed at x-2, etc. T-23.58sin(0.51x-1.79)+2.345 What is the average annual temperature for this community? A) 0.555°C OB) 2.345°C OC) 21.235°C (D) 25.925°Carrow_forward
- The daily cost to a printer is modeled by the function C(x) = 4x + 1400 where C(x) is the total daily cost and is the number of copies printed. Find C(7000), and interpret its meaning. C(7000) | Enter an integer or decimal number [more..] This value represents O The product of the daily cost and the number of copies O The number of copies manufactured when the daily cost is 7000 O The daily cost when 7000 copies are printed Check Answer masa Σarrow_forwardA closed box with a square bottom has a total surface area (all 6 sides) of 400 square inches. Express the volume of the box as a function of w. 40² Recall that the volume of a box with dimensions width, length, height is the product of all three. h 0 W 11 Ov(w) = w(200 - w²) Ov(w) = w(100 - 2w²) ○ v(w) = w(200 – w²) Ov(w) = w(100 – w²) -w(400 – w²) O V(W) =arrow_forwardThe height of a plant in inches is modeled by the linear function h(t)=3t+0.2 for the first year of growth. where t is the number of months since growth began, determine which of the following heights in not an example of extrapolation the answer choices are 80.2 inches 76.2 inches 56.2 inches 44.2 inches arrow_forward
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