Eloise has a piece of string that she cuts into smaller pieces. This line plot shows the lengths of the pieces. Matthew has a pi
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The right answer is C. never
The quotient of two algebraic expressions is a<em> fractional expression. </em> Moreover, the quotient of two <em>polynomials</em> such as:
is called a rational expression. So according to this definition rational expressions does not contain logarithmic functions. In fact, a rational expression is an expression that is the ratio of two polynomials like this:
Part A:
The average rate of change refers to a function's slope. Thus, we are going to need to use the slope formula, which is:
and
are points on the function
You can see that we are given the x-values for our interval, but we are not given the y-values, which means that we will need to find them ourselves. Remember that the y-values of functions refers to the outputs of the function, so to find the y-values simply use your given x-value in the function and observe the result:
Now, let's find the slopes for each of the sections of the function:
<u>Section A</u>
<u>Section B</u>
Part B:
In this case, we can find how many times greater the rate of change in Section B is by dividing the slopes together.
It is 25 times greater. This is because is an exponential growth function, which grows faster and faster as the x-values get higher and higher. This is unlike a linear function which grows or declines at a constant rate.