The concentration of a certain pollutant, c, (in parts per million or ppm) depends on the population of a city (in thousands of people). Let p be the population of Edmonton (in thousands of people) and let t be the number of years since 2010. These quantities are related according to: c=2.54p+98.55 and t=0.68p-18.91.
a. Define a function j that represents the population of Edmonton as a function of t, the number of years since 2010. Recall and use the complete function definition form.
b. Define a function k that represents the concentration of the pollutant (in ppm) as a function of p, the population of a city in thousands.
c. Define a function m that represents the concentration of the pollutant in Edmonton (in ppm) as a function of t. First define this function i) as an expression of j and k and t, and then ii) with a rule in terms of t that calculates the concentration.
d. Define a function n that represents the time in years since 2010 as a function of c, the concentration of the pollutant in Edmonton in ppm.
e. If the pollutant reaches 415 ppm, it is considered harmful. In what year will the pollutant become harmful in Edmonton?