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

Question

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

Accepted Answer

Hey, everyone here, we are asked to find the average rate of change that is illustrated in the given graph and determine what it means. Here, we have four answer choice options, ABC and D, each of which state that the average rate of change is either zero or undefined. And each solution has a description of what it means, having to do with the amount of spores spanned every day and whether it is a controlled or uncontrolled environment. So to begin solving this problem, we first need to recall the average rate of change formula which states that we need to take the Y final value minus the Y initial value. And then we divide this quantity by the X final value minus the X initial value. So now with this formula, we just need to look at our given points on our graph and select the first point as well as the last point to determine our X and Y values according to our formula. So starting with our first point, our initial point is zero and 135. This tells us that our X initial value is zero and our Y initial value is 135. Now, looking at the endpoint, the last point we are given is eight and 135. And this tells us that our X final value, our, our X final value is eight and our Y final value is 135. So now with our X and Y values clearly identified according to our formula, we can now just substitute in these values into the formula. And so we find that our average rate of change according to our given graph, we have 135 minus 135 all divided by eight minus zero. And now simplifying we get zero divided by eight, which tells us that our average rate of change for our graph is just zero. And now with our average rate of change being zero, this tells us that there is no increase in the amount of spores spawned every day. And therefore this tells us that we have a controlled environment. So with this information, we are left with answer choice D where again we have an average rate of, of change of zero and there is no increase in the number of spores spawned every day. Therefore, we know we have a controlled environment. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

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

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