2-1Casey.pdf - MATH1044 2.1 1 Change over Intervals...

This preview shows page 1 out of 6 pages.

Unformatted text preview: MATH1044 2.1 1 Change over Intervals Remember, a correct interpretation of a change measurement includes when, what, how, and by how much and includes units! 1. (Warm-Up) For the function f (x), • What is the change in f from x1 to x2 ? • What is the percent change in f from x1 to x2 ? • What is the average rate of change in f from x1 to x2 ? 2. The following table provides the price per gallon for regular unleaded gasoline in Ohio over 5 years. Year Price ($ per gallon) 2009 2.31 2010 2.72 2011 3.46 2012 3.56 2013 3.46 2014 3.24 (a) Find and interpret the percent change in the price of gas from 2010 to 2013. (b) Find and interpret the change in the price of gas from 2011 to 2012. (c) Find and interpret the average rate of change in the price of gas from 2009 to 2012. MATH1044 2 3. The temperature Y of a yam in a hot oven, t minutes after being placed there, is given by f (t) = 350 − 280(0.992t ) degrees F. (a) Compute f (60) and write a sentence of interpretation. (b) What is the percent change in the temperature of the yam in the first hour it is in the oven? Write a sentence interpreting your answer. (c) When we learned about exponential functions in 1.5, we said that the percentage change is (b − 1) · 100%. This seems to contradict your answer to (b) but it doesn’t - we mentioned the subtle detail in 1.5 but didn’t focus on it. How can both “percent change” answers be right? (d) What is the average rate of change in the temperature of the yam over the first 10 minutes? Write a sentence interpreting your answer. MATH1044 3 4. For the second quarter of 2009, an airline posted revenue of $603.1 million, compared with revenue of $693.9 million during the second quarter of 2008. (a) What is the percent change in the airline’s revenue in this time period? Include units. (b) What is the average rate of change in the airline’s revenue in this time period? Include units. 5. The graph below shows f (x), the temperature of a solution during an experiment, and also the line g(x). 6 5 g(x) f(x) 4 3 2 1 10 20 30 x Which of the following represent the slope of g(x)? Check ALL correct answers.  the average temperature from the 10th to the 25th hours.  the change in temperature from the 10th to the 25th hours.  the exact rate of temperature change from the 10th to the 25th hours.  the average rate of temperature change from the 10th to the 25th hours.  the slope of a secant line of f (x).  the slope of an asymptotic line of f (x). MATH1044 4 6. The population P of a town t years after 2005 is given in the graph below. 24 P (thousands) 20 16 12 8 4 0 0 1 2 3 t (years) 4 5 6 (a) What is the change in the population from 2005 to 2009? (b) What is the average rate of change in the population from 2009 to 2011? (c) Draw the secant line connecting (2, P (2)) and (5, P (5)). Find the slope of this line and write a sentence of interpretation for it. 7. The number of internet users in Mexico between 2004 and 2008 can be modeled as u(t) = 8.02(1.17t ) million users, where t is the number of years since 2004. What is the average rate of change in the number of internet users in Mexico from 2004 to 2008? Include units in your answer. MATH1044 5 8. Find a sine model formula for the function f (x) who graph is below. f(x) 4 3 2 1 1 2 3 4 5 6 7 x -1 9. Find the inverse function t(g): g(t) = −1 + x−4 . 3x + 2 MATH1044 6 10. The daily mean temperature in Fairbanks, Alaska oscillates with a low of 12◦ F on the 10th day of the year and a high of 62◦ F on the 192nd day of the year. Find a sine model for f (t), the daily mean temperature in Fairbanks on the tth day of the year. 11. A bacteria population is growing at a rate of 1.8% per hour. If there were 4.5 million bacteria at noon, how many bacteria were there at 5pm? ...
View Full Document

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture