Formulas Quantifying Change

Thomas J. Pfaff ()
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Thomas J. Pfaff: Ithaca College, Department of Mathematics

Chapter Chapter 6 in Applied Calculus with R, 2023, pp 65-76 from Springer

Abstract: Abstract We continue with the CO2 function example from chapter 4 chapter and provide some context about changing atmospheric CO2 levels by using different formulas to quantify change. We will focus on the period of the data, which is 1950 to 2017. The total change, M-Box 6.1, in CO2 levels from 1950 to 2017 is $$ CO2(67)\, \text {ppm}-CO2(0)\, \text {ppm} = 95.3 \, \text {ppm}.$$ C O 2 ( 67 ) ppm - C O 2 ( 0 ) ppm = 95.3 ppm . In other words, from 1950 through 2017 atmospheric CO2 levels increased by 95.3 ppm. A related calculation is the average rate of change over a time period, M-Box 6.2. In this case $$ (CO2(67)\,\text {ppm}-CO2(0)\,\text {ppm})/(67 \, \text {year} - 0 \, \text {year}) = 1.42 \text {ppm per year}.$$ ( C O 2 ( 67 ) ppm - C O 2 ( 0 ) ppm ) / ( 67 year - 0 year ) = 1.42 ppm per year . In other words, from 1950 through 2017 CO2 levels increased on average by 1.42 ppm per year. Two details to note. First, the input for the CO2(t) function is years after 1950, but when we report the results we don’t say 67 years after 1950; we say 2017. Similarly, we use year as the unit in the denominator in the calculation in 6.1. The average rate of change is also the slope of the secant line, as seen in Chapter 4 , and averages the change over the time period. This does not mean CO2 necessarily increased by 1.42 ppm per year as this is the yearly average over that time period.

Date: 2023
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DOI: 10.1007/978-3-031-28571-4_6

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