A gardener at a nursery is filling pots with soil to prepare to transplant seedlings into these larger pots. Each new pot needs about 27 cubic inches of soil. The amount of soil s (in cubic inches) it takes to fill p pots is given by the function s 5 27p.
a. The gardener is filling the pots from a bag of soil that contains 3456 cubic inches of soil. Graph the function and identify its domain and range. How many pots can be filled from the bag?
b. Suppose the gardener needs to fill 100 pots. Graph the function on the same coordinate plane in part (a) and identify its domain and range. How much soil (in cubic inches) will the gardener need
I DID IT NEVER MIND
a. To graph the function s = 27p, we can plot points by choosing values for p and calculating the corresponding values for s.
Let's choose a few values for p:
- p = 0: s = 27 * 0 = 0
- p = 1: s = 27 * 1 = 27
- p = 2: s = 27 * 2 = 54
- p = 3: s = 27 * 3 = 81
Now, let's plot these points on a coordinate plane.
- The domain of the function is the set of possible values for p, which in this case would be all non-negative integers since you can't have a negative number of pots.
- The range of the function is the set of possible values for s, which starts from 0 (when p = 0) and increases in increments of 27.
Since we know that the bag of soil contains 3456 cubic inches of soil, we can find out how many pots can be filled from the bag by solving the equation s = 3456 for p:
27p = 3456
Dividing both sides by 27:
p = 3456 / 27 ≈ 128
Therefore, the gardener can fill approximately 128 pots from the bag of soil.
b. If the gardener needs to fill 100 pots, we can repeat the above steps to find the corresponding values for s:
p = 100
s = 27 * 100 = 2700
Now, let's add this point to the graph from part (a).
- The domain remains the same (all non-negative integers).
- The range would be from 0 to 2700 (inclusive).
To find out how much soil the gardener will need, we can simply look at the value of s when p = 100, which is 2700 cubic inches.