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What is the average rate of change of the function on the interval from x = 1 to x = 2?

f(x)=10(5.5)x



Enter your answer, as a decimal, in the box.

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Calniz
Hey there, Rileydavidson18!

To find the rate of change when x = 1 and when x = 2, we need to find the values of the f(x) when x is equal to 1 and 2.

f(x)=10 (5.5)^x

Now, to find the rate of change we need to use the formula [tex] \frac{y2-y1}{x2-x1} [/tex]
So, it should be [tex] \frac{302.5-55}{2-1} [/tex] which would give you [tex] \frac{247.5}{1} [/tex] which is the same as 247.5
So, the rate for the interval [1,2] is equal to 247.5

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JabbaTheHut
The equation to calculate the average rate of change is: y/x

y = f(x2) - f(x1)
x = x2 - x1

x1: 1 (The smaller x value. It can be any number)
x2: 2 (The larger x value. It also can be any number)
f(x1): The value when you plug x1 into the function.
f(x2): The value when you plug x2 into the function.

If we know this, the variables for this problem are assuming the function is 10(5.5)^x:

x2: 2
x1: 1
f(x2): 10(5.5)^(2) = 302.5
f(x1): 10(5.5)^(1) = 55

This means:
y = 302.5  - 55 = 247.5
x = 2 - 1 = 1

Remember: the equation for avg rate of change is y/x

So, our average rate of change for the function on the interval [1,2] is 247.5 (y/x = 247.5/1)

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