Algebra II : Extrapolations
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Example Questions
Example Question #451 : Basic Statistics
What is the next number in this sequence: 8, 27, 64, 125 ?
Find the pattern of the sequence:
This pattern is 
Example Question #452 : Basic Statistics
Find the next 2 numbers in this sequence: 33, 46, 72, 111
Find the pattern in this sequence of numbers:
In this case, the pattern is adding 13n to the previous number where n= how many numbers came before the current number.
so the first number we are looking for would be:
the second number we are looking for would be:
Example Question #1 : Extrapolations
The amount of water inside of a leaky boat is measured periodically after the boat has been in the water in different periods of time and are found to have a linear relationship. The results are given in the following chart:
| Time in water (mins) | Amount of water in the boat (gal) |
| 0 | 0 |
| 6 | 4.8 |
| 19 | 15.2 |
| 28 | 22.4 |
Using the method of linear extrapolation based on the data from the table, how much water would you expect to be in the boat after 
To extrapolate the results of the study out to 53 minutes, first we have to determine an equation representing the relationship between time passed and amount of water; we can write our equation in slope-intercept form:
Where our y-axis represents amount of water and the x-axis represents time. We can pick 2 points and label them Point 1 and Point 2; looking back at the table:
| Time in water (mins) | Amount of water in the boat (gal) |
| 0 | 0 |
| 6 | 4.8 |
| 19 | 15.2 |
| 28 | 22.4 |
We label Point 1 as 
So, the slope of our line that describes how much water is in the boat is 
Simplify the expression and we find that b=0, so our slope-intercept equation is:
Plugging in a value of 53 for 
So the answer is 42.4 gallons of water in the boat after 53 minutes.
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