Question

length (minutes) : |1.5 | | 2 | | 3 | | 4.5 |
amount of water (gallons): |3,700| |4,100| |6,450| |8,400|
Old Faithful is a geyser in Yellowstone National Park. The table shows the approximate length of an eruption (in minutes) and the amount of water (in gallons) in that eruption.

What is the BEST interpretation of the slope in context of this problem?
Responses
A Each additional minute in eruption length results in a prediction of an additional 1,350 gallons of water produced.Each additional minute in eruption length results in a prediction of an additional 1,350 gallons of water produced.
B Each additional minute in eruption length results in a prediction of an additional 1,567 gallons of water produced.Each additional minute in eruption length results in a prediction of an additional 1,567 gallons of water produced.
C That the minimum amount of water produced for each additional minute in eruption length is 1,867 gallons.That the minimum amount of water produced for each additional minute in eruption length is 1,867 gallons.
D That the maximum amount of water produced for each additional minute in eruption length is 2,467 gallons.

Answer 1

To find the best interpretation of the slope in context, we first need to calculate the slope of the line that fits the given data. The points from the table represent eruption lengths and corresponding amounts of water:

- (1.5, 3700)
- (2, 4100)
- (3, 6450)
- (4.5, 8400)

The slope (m) can be found using the formula:

\[
m = \frac{{\text{{change in amount of water}}}}{{\text{{change in eruption length}}}}
\]

We can compute the slope using the two points that provide the change in both variables. Let's take the points (1.5, 3700) and (4.5, 8400):

\[
\text{{change in amount of water}} = 8400 - 3700 = 4700 \text{ gallons}
\]
\[
\text{{change in eruption length}} = 4.5 - 1.5 = 3 \text{ minutes}
\]

Now, we can substitute these values into the slope formula:

\[
m = \frac{{4700}}{{3}} \approx 1566.67 \text{ gallons per minute}
\]

Rounding this value gives us approximately 1,567 gallons per minute.

Therefore, the best interpretation of the slope in context of the problem is:

**B Each additional minute in eruption length results in a prediction of an additional 1,567 gallons of water produced.**