PLEASE I NEED HELP:
the number of seniors citizen (65 an over)in the united states are millions įN years after 1990 can be estimated by using the function:
s=0.38į +31.2
the percentage of senior citizen living below the poverty level Nį years after 1990 can be estimate using the function p=-0.25į+12.2
What is the first year in which we can expect both the number of seniors to be greater than 37 million and fewer than 7% living below the poverty level? Round all immediate calculation to one decimal place and round Nį in the final calculation to the nearest whole number?
To find the first year in which we can expect both the number of seniors to be greater than 37 million and fewer than 7% living below the poverty level, we need to solve the following system of equations:
1) The number of seniors equation: s = 0.38į + 31.2
2) The percentage of seniors below poverty equation: p = -0.25į + 12.2
We want to find the year (į) for which both s > 37 million and p < 7%.
First, let's tackle the number of seniors equation (1):
s = 0.38į + 31.2
Since we want s to be greater than 37 million, we can set up the following inequality:
0.38į + 31.2 > 37
Next, we'll solve this inequality for į:
0.38į > 37 - 31.2
0.38į > 5.8
Now divide both sides by 0.38 to isolate į:
į > 5.8 / 0.38
į > 15.263
Since į represents years, we'll round this up to the nearest whole number, so į > 16.
Now let's move on to the percentage of seniors below poverty equation (2):
p = -0.25į + 12.2
Since we want p to be less than 7%, we can set up the following inequality:
-0.25į + 12.2 < 7
Next, we'll solve this inequality for į:
-0.25į < 7 - 12.2
-0.25į < -5.2
Now divide both sides by -0.25, but remember to reverse the inequality sign since we're dividing by a negative:
į > (-5.2) / (-0.25)
į > 20.8
Again, since į represents years, we'll round this up to the nearest whole number, so į > 21.
To find the first year that satisfies both conditions, we need to find the smallest common whole number that satisfies both inequalities. In this case, it is 21.
Therefore, the first year in which we can expect both the number of seniors to be greater than 37 million and fewer than 7% living below the poverty level is 21 years after 1990.