Find and interpret the average rate of change illustrated in each...

Question

Find and interpret the average rate of change illustrated in each graph.

Graph showing Company X's bi-yearly carbon production rate over 10 years with data points.

Accepted Answer

Hello everybody. Everything right. Today, today, we're going to be looking at this question that states consider the given graph where our graph on the Y axis has company X activated carbon by yearly production rates in tons. And on the X axis, we have the year, the year stretching from 0 to 10 and the Y axis stretching from to 450. And we have a line increasing upwards at a constant rate with points at two comma 94 comma 86 comma 2 78 comma 3 60. Now the question states what is the average rate of change illustrated? And what does it mean the estruses provided are a average rate of change equals 45 tons per year, which means activated carbon production rate is increased by 45 tons every year. Average choice B states average rate of change equals 45 tons per year. Meaning activated carbon production rate is in, is decreased by 45 tons every year. A choice C states average rate of change equals 2, 22.5 tons per year. Meaning activated carbon production rate is increased by 22. tons every year. And as the choice D states average rate of change equals 22 tons per year. Meaning activated carbon production rate is decreased by 22. tons every year. Now, first, we have to ask ourselves, what does average rate of change mean? So average rate of change, average rate of change is equal to Y final minus Y initial and all that divided by X final minus X initial. So what do those mean in our case are Y final is equal to? Well, let's look at our line, the last Y value they give us or our line reaches is 360. That's the last point that we have. So our Y final will be R Y initial is the first Y given to us, which is zero. Our line starts at the origin. So we have a Y of zero at the origin. Now for X final, we do the same thing but look at the X values. Our, our last Y value given to us was 360 the X component of that was eight. So our final is eight. Now for the X initial, we do the same thing. Look at the first X value given to us. And like I, like we mentioned, the line starts at the origin which has an X of zero. So now that we have a value for each variable, we can plug, plug them in into our equation. So we have Y final, which is 360 minus Y initial, which is zero. And that would be in the numerator. And that's divided by X final, which is eight minus X initial initial with it, which is zero. So 360 minus zero is 360 divided by eight minus zero, which is eight. And we'll be left, we're left with 360 divided by eight, which is 45. And now we have to assign units to this. So we had Y values divided by X values. So we just have to look at the axis are Y axes is tons. If we just read what they told us, company X activated carbon by yearly production rate in tons. So we'll have tons in the numerator of our rate. So we'll have 45 tons per because the denominator was the X values. Now, we see what the X axis was labeled and it was labeled year. So it'll be 45 tons per year and that'll be the average rate of change. And what does this mean? Well, I'll scroll down a bit so we can see the answer more clearly. Since we have 45 tons per year, we can eliminate answer choice C and answer choice D since they have 22.5. Now we have to decide between A and B. Well, our answer is positive and our line is increasing upwards. Meaning that the production rate is increasing. If it was negative or the line was decreasing, then the pro the rate of change would also be decreasing. So we're left with answer choice. A average rate of change equals 45 tons per year. Meaning that the activated carbon production rate is increased by 45 tons every year. So I hope that was helpful. And until next time.

Find and interpret the average rate of change illustrated in each graph.

Key Concepts

Average Rate of Change

Linear Functions

Graph Interpretation

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