To analyze the given equations for the number of men and women receiving bachelor’s degrees from 1970 to 2014, we can break down the provided equations:
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For men receiving bachelor's degrees: \[ y = 3.9x + 443 \]
- Here, \(y\) represents the number of men receiving degrees (in thousands).
- \(x\) is the number of years after 1970.
- Hence, for \(x = 0\) (year 1970), \(y = 443\) (thousand men).
- For each year, approximately 3.9 thousand more men receive degrees.
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For women receiving bachelor's degrees: \[ y = 14.3x + 316 \]
- Here, \(y\) represents the number of women receiving degrees (in thousands).
- Again, \(x\) is the number of years after 1970.
- For \(x = 0\) (year 1970), \(y = 316\) (thousand women).
- For each year, approximately 14.3 thousand more women receive degrees.
Find degrees awarded in a specific year
To find the number of degrees awarded in a particular year, substitute the value of \(x\) into the equations.
Example: To find the number of degrees awarded in 2014:
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In 2014, \(x = 2014 - 1970 = 44\).
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For men: \[ y = 3.9(44) + 443 = 171.6 + 443 = 614.6 \] Thus, approximately 614,600 men received bachelor's degrees in 2014.
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For women: \[ y = 14.3(44) + 316 = 631.2 + 316 = 947.2 \] Thus, approximately 947,200 women received bachelor's degrees in 2014.
Summary of Trends
From the analysis of the trends:
- The number of men receiving bachelor's degrees has increased from 443,000 in 1970 to approximately 614,600 in 2014.
- The number of women receiving bachelor's degrees has risen significantly from 316,000 in 1970 to approximately 947,200 in 2014.
- The increase per year is notably larger for women than for men, indicating a faster growth rate in the number of women obtaining bachelor’s degrees during this period.