An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (1)
Calculate the average rate of change for 2009-2011: 2011 − 2009 19 − 9 = 5 .
Calculate the average rate of change for 2011-2012: 2012 − 2011 17 − 19 = − 2 .
Calculate the average rate of change for 2012-2016: 2016 − 2012 177 − 17 = 40 .
The average rates of change are 5 , − 2 , and 40 , respectively. 5 , − 2 , 40
Explanation
Understanding the Problem We are given a table showing the number of sexual violence complaints in U.S. Higher Ed from 2009 to 2016. Our task is to calculate the average rate of change in the number of complaints for the periods 2009-2011, 2011-2012, and 2012-2016. We need to round all values to the nearest whole number.
Formula for Average Rate of Change To find the average rate of change between two years, we use the formula: Average Rate of Change = Change in Years Change in Complaints We will apply this formula to each of the specified periods.
Calculating Rate of Change (2009-2011) For the period 2009-2011: Average Rate of Change = 2011 − 2009 Complaints in 2011 − Complaints in 2009 = 2011 − 2009 19 − 9 = 2 10 = 5 So, the average rate of change from 2009 to 2011 is 5 complaints per year.
Calculating Rate of Change (2011-2012) For the period 2011-2012: Average Rate of Change = 2012 − 2011 Complaints in 2012 − Complaints in 2011 = 2012 − 2011 17 − 19 = 1 − 2 = − 2 So, the average rate of change from 2011 to 2012 is -2 complaints per year.
Calculating Rate of Change (2012-2016) For the period 2012-2016: Average Rate of Change = 2016 − 2012 Complaints in 2016 − Complaints in 2012 = 2016 − 2012 177 − 17 = 4 160 = 40 So, the average rate of change from 2012 to 2016 is 40 complaints per year.
Final Answer The average rates of change for the specified periods are:
2009-2011: 5
2011-2012: -2
2012-2016: 40
Examples
Understanding rates of change is crucial in many real-world scenarios. For instance, in economics, it helps analyze the growth rate of a country's GDP or the inflation rate. In environmental science, it can be used to track the rate of deforestation or the increase in global temperatures. In public health, like the example in the problem, it helps to monitor the increase or decrease in the number of reported cases of a certain disease or incidents, allowing for timely interventions and resource allocation. The concept of rate of change provides valuable insights for informed decision-making across various fields.
