Let's tackle the problem step by step.
1) Fill out the table below
To find the amount of food left (y) after a certain number of days (x), we can use the relation:
\[ y = 360 - 12x \]
Now we can fill in the table:
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For x = 0 (starting point): \[ y = 360 - 12(0) = 360 \]
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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: \[ y = 360 - 12(15) = 360 - 180 = 180 \]
So the table is:
\[ \begin{array}{|c|c|} \hline x & y \ \hline 0 & 360 \ 5 & 300 \ 10 & 240 \ 15 & 180 \ \hline \end{array} \]
2) Write the equation in slope-intercept form of this situation
The equation relating \(x\) (days) to \(y\) (amount of food left) is:
\[ y = 360 - 12x \]
This equation is already in slope-intercept form \(y = mx + b\), where:
- \(m = -12\) (the slope, indicating the amount of food consumed per day)
- \(b = 360\) (the y-intercept, indicating the initial amount of food)
3) In how many days will the hikers run out of food?
The hikers will run out of food when \(y = 0\):
\[ 0 = 360 - 12x \]
To solve for \(x\):
\[ 12x = 360 \] \[ x = \frac{360}{12} = 30 \]
The hikers will run out of food in 30 days.
1 answer