Let’s tackle the questions one by one.
1) Fill out the table below
We start with 360 pounds of food and the hikers eat 12 pounds per day. We can calculate the amount of food left (y) after x days using the formula:
\[ y = 360 - 12x \]
Now we will fill in the table for the given values of x.
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For x = 0: \[ y = 360 - 12(0) = 360 \]
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For x = 5: \[ y = 360 - 12(5) = 360 - 60 = 300 \]
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For x = 10: \[ y = 360 - 12(10) = 360 - 120 = 240 \]
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For x = 15: \[ y = 360 - 12(15) = 360 - 180 = 180 \]
Now, we can summarize the table:
| x | y | |-----|-----| | 0 | 360 | | 5 | 300 | | 10 | 240 | | 15 | 180 |
2) Write the equation in slope-intercept form of this situation
The equation we derived earlier can be expressed in slope-intercept form \(y = mx + b\), where:
- \(m\) is the slope (the rate of food consumption),
- \(b\) is the y-intercept (the initial amount of food).
From our formula \(y = 360 - 12x\):
- The slope \(m = -12\) (meaning they consume 12 pounds per day),
- The y-intercept \(b = 360\) (the initial quantity of food).
Thus, the equation in slope-intercept form is:
\[ y = -12x + 360 \]
3) In how many days will the hikers run out of food?
The hikers will run out of food when \(y = 0\). We can set the equation to zero and solve for \(x\):
\[ 0 = 360 - 12x \]
Rearranging this gives:
\[ 12x = 360 \]
Now, dividing both sides by 12, we find:
\[ x = \frac{360}{12} = 30 \]
Therefore, the hikers will run out of food in 30 days.
To summarize:
- The table is filled out and presented above.
- The equation is \(y = -12x + 360\).
- The hikers will run out of food in 30 days.
1 answer