A local zoo has just opened a new stingray environment with 7 young, healthy stingrays. The population of stingrays in the enclosure is expected to at least double every year and can be represented after x years by this inequality.𝑦≥7(2)𝑥At the time the stingrays were added to the enclosure, the zookeepers determined that the enclosure could sustain at most 160 stingrays. The number of stingrays the enclosure can sustain after x years, because of budget constraints, can be represented by this inequality.𝑦≤160−2𝑥Which point on the graph represents a possible number of stingrays, y, in the enclosure?
Question
A local zoo has just opened a new stingray environment with 7 young, healthy stingrays. The population of stingrays in the enclosure is expected to at least double every year and can be represented after x years by this inequality.𝑦≥7(2)𝑥At the time the stingrays were added to the enclosure, the zookeepers determined that the enclosure could sustain at most 160 stingrays. The number of stingrays the enclosure can sustain after x years, because of budget constraints, can be represented by this inequality.𝑦≤160−2𝑥Which point on the graph represents a possible number of stingrays, y, in the enclosure?
Solution
To find a possible number of stingrays, y, in the enclosure, we need to find a point that satisfies both inequalities.
The first inequality, y ≥ 7(2)^x, represents the population growth of the stingrays. The second inequality, y ≤ 160 - 2x, represents the maximum number of stingrays the enclosure can sustain.
We need to find a point (x, y) that satisfies both inequalities. This means we need to find a year, x, and a number of stingrays, y, such that the population of stingrays is at least double the previous year's population but also less than or equal to the maximum number the enclosure can sustain.
Without specific points provided, we can't give a specific answer. However, we can say that any point that lies in the region where both inequalities overlap on a graph would represent a possible number of stingrays in the enclosure.
To find these points, you would graph both inequalities on the same set of axes and look for the region where they overlap.
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