The Inflation Rate

Synopsis:
Great Grandpa Juan died on May 23, 2013. Juan Jr. Jr. purchased a coffin for him to be buried in. The next year Juan Jr. Jr. was learning about inflation rates, and was interested in knowing how much more the coffin would have cost if Great Grandpa Juan had died later. To find this out, Juan must calculate the instantaneous rate of change in May in order to ascertain the change in the inflation rate. What was the instantaneous rate of change in may?

Table:

Graph:

Average Rate of Change: when x=5
(5, 1.4) and (4, 1.1)   (1.4-1.1)/ (5-4)=     .3
(5,1.4) and (6,1.8) (1.4-1.8)/(5-6)=               .4
(5,1.4) and (7,2) (1.4-2)/(5-7)=         .3
The average rates of change calculated show the approximate change in the inflation rate over a certain period of time, and will be helpful to Juan Jr. Jr. when trying to figure out the average change in inflation over time. These results will give him a better idea as to what the instantaneous rate of change is and a greater overall view of the monthly changes in inflation.

Instantaneous Rate of Change:
(5,1.4) and (5.5,1.6) (1.4-1.6)/(5-5.5)=     .4
By calculating the Instantaneous rate of change, Juan Jr. Jr. learned that the inflation rate in May was increasing by .4% at that given moment, which means that the price of the coffin would have been about. 4% higher if Great Grandpa Juan had passed away at a later date.

Explanation:
Juan Jr. Jr. knows that the value he calculated as the IRC is in fact correct because as the intervals decreased when calculating the ARC they were approaching .4. Because these match up, Juan knows that his calculations are correct and that in the month of May, the inflation rate was increasing by .4 % when Juan found this out, he thanked his Great Grandpa for dying when he did, and consequently saving him money.