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Problem 49

The table shows world average daily oil consumption from 1985 to 2010 measured in thousands of barrels per day.

(a) Compute and interpret the average rate of change from 1990 to 2005. What are the units?

(b) Estimate the instantaneous rate of change in 2000 by taking the average of two average rates of change. What are its units?

Answer

(a) 1169.6

(b)1397.8

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## Discussion

## Video Transcript

this problem. Number forty nine of the Stuart Calculus eighth edition Section two seven The table shows world average daily oil consumption from nineteen eighty five to two thousand ten, measured in thousands of barrels. Pretty party Computer's interpret the average reader change from nineteen ninety two thousand five. So if we look at the chart, the first column is years since nineteen. Eighty five. Zero years since nineteen eighty five is nineteen eighty five. So there's nineteen eighty five five years afterwards, his nineteen ninety. And then it goes by big five year increments. So nineteen, ninety ninety. Ninety five. Two thousand two thousand five two thousand ten. So these are the thousands of barrels of oil per day that correspond teacher these years and in party, we're going to compute. The average rate of change from nineteen ninety two thousand five nineteen ninety is five years since then. Painted. Five. Two thousand fine is twenty years since nineteen eighty five. So we're going to use thes two values here and compute the average rate of change. The the first value. Eighty four zero seven. The second value. Sixty six five thirty three a four zero seven seven Parting in the second part. Sixty six five eight three eighty four zero seven seven is the two thousand and five quantity and six sixty six five three is it doesn't are our is the nineteen ninety quantity. So there's a difference of fifteen years. There s so if we take this ratio, we should get approximately once one six, nine point six, which is almost one one seven zero. And we're going to say this is ah, thousands of barrels, thousands of barrels per day, That scene you know, since we divided by Eater's as well we're going to say per day per year and those of the inn it's for parts are being estimate the instantaneous rate of change of in two thousand ten by taking the average of two rates of change so it doesn't or two thousand two thousand seventeen to ten injury in two thousand two thousand wass fifteen years actions or since nineteen eighty five I'm so two dozen is this part here. But in order to find the instantaneous hurry to change her to estimate it, we're going to take the average rate of change. Ah, the previous interval, which is nineteen. Ninety five to two thousand five and then the other average ready to change from two thousand two. Two dozen five. Nineteen ninety five to two thousand. Two thousand to two thousand. Fine. Those savages. Rates of change. We're going to take the average of King. So the first part from nineteen ninety five two thousand it goes from seventy thousand zero nine nine thousands of barrels of oil per team. Two. Seventy six seven eighty four thousands of barrels of oil per day. I'm so seventy six seventy four minus seventy thousand ninety nine and then going from nineteen. Ninety five to two thousand this five years. So calculating this, we get six hundred for attorney there. Referee thirteen. Thirty seven. It will save thousands barrels for you. Good day here. Okay, The second rate of change is from two thousand to two thousand Fire. So there goes seventy six seven eighty four up until eight. Eighty four thousand seventy. Eighty. Eighty four thousand seven minus seventy six seventy four rather by five years. And if we do the calculation, we get approximately fourteen pounds. Fourteen hundred fifty things. One six thousands of barrels of oil her day. Hurry in here So these are the children's things to change before and after two thousand. If we take the average of these two numbers that we just calculated, we should have get approximate, um, estimate for the instantaneous would've changed in two thousand. So the average of these numbers comes up to be thirteen eighty seven point eight thousands of barrels of oil per day per year. That is our final.

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