In response to rising concerns about identity theft the number of models of paper shredders accompany manufactures increased approximately steadily from five models in 1999 to 33 models in 2007. Find the average rate of change of the number of shredder models manufactured per year between 1999 and 2007.
To find the average rate of change of the number of shredder models manufactured per year between 1999 and 2007, we need to calculate the total change in the number of models and divide it by the number of years.
The total change in the number of models is obtained by subtracting the initial value from the final value:
Total change = Final value - Initial value
In 1999, there were 5 models of paper shredders, and in 2007, there were 33 models. Therefore:
Total change = 33 - 5 = 28
The number of years between 1999 and 2007 is:
Number of years = 2007 - 1999 = 8
Now, divide the total change by the number of years to find the average rate of change:
Average rate of change = Total change / Number of years
Average rate of change = 28 / 8
Average rate of change = 3.5
Therefore, the average rate of change of the number of shredder models manufactured per year between 1999 and 2007 is 3.5.
To find the average rate of change of the number of shredder models manufactured per year between 1999 and 2007, we need to calculate the change in the number of models and divide it by the number of years.
The change in the number of models is given by:
Change in number of models = Number of models in 2007 - Number of models in 1999
Number of models in 2007 = 33
Number of models in 1999 = 5
Change in number of models = 33 - 5 = 28
The number of years between 1999 and 2007 is 2007 - 1999 = 8 years.
Average rate of change = Change in number of models / Number of years
Average rate of change = 28 / 8 = 3.5 models per year
Therefore, the average rate of change of the number of shredder models manufactured per year between 1999 and 2007 is 3.5.
To find the average rate of change of the number of shredder models manufactured per year between 1999 and 2007, we need to calculate the change in the number of shredder models and divide it by the change in years.
Let's denote the number of shredder models in a given year as M, and the year as t.
In 1999, the number of shredder models is M1 = 5, and the year is t1 = 1999.
In 2007, the number of shredder models is M2 = 33, and the year is t2 = 2007.
The change in shredder models is ΔM = M2 - M1 = 33 - 5 = 28.
The change in years is Δt = t2 - t1 = 2007 - 1999 = 8.
Now, calculate the average rate of change (ARoC) using the formula:
ARoC = ΔM / Δt
ARoC = 28 / 8
ARoC = 3.5
Therefore, the average rate of change of the number of shredder models manufactured per year between 1999 and 2007 is 3.5 models per year.