Concept explainers
Health-Care Spending in the 1990s Write
a. Find a linear model for the rate of change
b. Given that $700 billion was spent on health care in the United States in 1990, find the function
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Applied Calculus
- For the following exercise, consider this scenario: In 2004, a school population was 1,700. By 2012 the population had grown to 2,500. Assume the population is changing linearly. a. How much did the population grow between the year 2004 and 2012? b. What is the average population growth per year? c. Find an equation for the population, P, of the school t years after 2004.arrow_forwardWhat is extrapolation when using a linear model?arrow_forwardSuppose the world’s oil reserves in 2014 are 1,820 billion barrels. If, on average, the total reserves are decreasing by 25 billion barrels of oil each year: a. Give a linear equation for the remaining oil reserves,R, in terms of t, the number of years since now. b. Seven years from now, what will the oil reserves be? c. If the rate at which the reserves are decreasing is constant, when will the world’s oil reserves be depleted?arrow_forward
- Sales Barnes & Noble had annual sales of $6.8 billion in 2013 and $6.1 billion in 2015. Use the Midpoint Formula to estimate the sales in 2014. Assume that the annual sales followed a linear pattern.arrow_forwardSound Speed in Oceans Marine scientists use a linear model for the speed c of sound in the oceans as a function of the salinity S at a fixed depth and temperature. In the following table, one scientist recorded data for c and S at a depth of 500 meters and a temperature of 15 degrees Celsius. Here c is measured in meters per second and S in part per thousand. Salinity S Sound speed c 35.0 1515.36 35.6 1516.08 36.2 1516.80 36.8 1517.62 37.4 1518.24 a. Looking over the table, the scientist realizes that one of the entries for sound speed is in error. Which entry is it, and what is the correct speed? b. Explain in practical terms the meaning of the slope of the linear model for c in terms of S at the given depth and temperature. c. Calculate c39 and explain in practical terms what it means.arrow_forwardNeurology The average weight of a male child’s brain is 970 grams at age 1 and 1270 grams at age 3. (a) Assuming that the relationship between brain weight y and age t is linear, write a linear model for the data. (b) What is the slope and what does it tell you about brain weight? (c) Use your model to estimate the average brain weight at age 2. (d) Use your school’s library, the Internet, or some other reference source to find the actual average brain weight at age 2. How close was your estimate? (e) (d) Do you think your model could be used to determine the average brain weight of an adult? Explain.arrow_forward
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