average cola consumption?

Question

I'm given the equation S(t) = 6e^[(ln 2)(t)]. S(t) is billions of gallons of cola consumed per year and t is measured in years from the beginning of 1980. Thus the year 1980 for t would be 0, for 1981 t = 1 etc. I'm asked to find the average rate of consumtion over the 10 year time period beginning in 1983. I'm not sure if i should integratethe rate of cola consumption to get the average or what to do really. then is asks me what the integral of S(t) represents and I'm not really sure what that would be either, maybe how much cola is consumed vs the rate at which it's consumed? HELP!

Answer 1

You do indeed have to integrate the function from 3 to 13 and divide by 10 to get the average consumption for the 10 year period. The integral represents the total amount consumed in the time period.