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For the function with the greatest rate of change, what is the value when x = 10

For the function with the greatest rate of change, what is the value when x = 10-example-1
User Soger
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10 votes

It's 28.

So first, you need to calculate the rate of change, or slope, for each of the equations. You also need to put each of them into equation form, using the y=mx+b formula, but you can't do that without knowing the slope, or rate of change. Please note, the rate of change in this answer will be referred to as slope and the initial value will be referred to as y-intercept.

For the first one, the equation is already written for you. The slope in the equation is 5/2, or 2.5 in decimal form.

For the second one, we start at knowing 0=1, so the y intercept is 1. So then we see that 1=3/2, or 1.5 in decimal form. So, we just find the difference between 1 and 1.5, which is 0.5. We can now write our equation, y=0.5x+1.

The third one is the hardest one to calculate. We see the initial value, or the y intercept is 2. So far we have y=mx+2. Now, we have to figure out the slope, or rate of change. So, we see that 0=2. Now, let's look at another point in the graph. We'll do 2,5 since it is a clear point. So, here, the y value is 5. Let's subtract 5-2, and we get 3. However, we are not done. Because we chose a clear point in the graph to compare, we jumped 2 x spaces ahead, not one. So, now we divide by 2 to equal that out. So, 5/2=1.5. The slope is 1.5. Now, we have our equation, y=1.5x+2.

Now, we just compare our slopes, or rate of change to each other to find the greatest. We have 2.5, 0.5 and 1.5. 2.5 is the greatest. That was the first one. Now, it is asking us what the y value would be if x equals 10. So, we can just plug in 10 where x is in the equation. So, y=10x2.5+3. 10x2.5=25 and then plus 3 is 28. So, that is your answer.

I hope this helps you answer the problem.

User Pajeh
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