A rabbit hops 8 meters in one second. After 7 seconds, the rabbit has hopped 20 meters. What is the rabbit's average rate of cha
1 answer:
Answer:
Average Rate of change = 2
Step-by-step explanation:
Given - A rabbit hops 8 meters in one second. After 7 seconds, the rabbit has hopped 20 meters.
To find - What is the rabbit's average rate of change?
Formula used -
Average rate of change of a function f(x) in an interval [a, b] is
Proof -
Given that,
In 1 second - Rabbit hoops 8 meters
In 7 seconds - Rabbit hoops 20 meters
So,
Average Rate of change =
=
= 2
⇒Average Rate of change = 2
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The average rate of change on the interval (5, 6) is 9. So the correct option is D.
<h3>How to find the average rate of change on the interval?</h3>
Here we want to find the average rate of change of f(x), the function on the table, on the interval (5, 6).
This is just:
I we look at the table we see that:
This is a system of equations.
If we subtract the second and first functions, we get:
From that we take two relations:
Now we can replace these two in the last equations so we get:
Now that we know the value of a:
The quadratic equation is:
Evaluating this in x = 6 we get:
And from the table we know that f(5) = 17, then the average rate of change is:
The correct option is D.
If you want to learn more about average rates of change:
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Answer:
Step-by-step explanation:
Given that t represents a number which is unknown to us, the difference of the number and 9 can be expressed algebraically as:
.
The difference of t and 9 = .