non linear systems of equations

[figuresk8rgirl]

Year Percent Male
1960 65.8
1965 61.5
1970 59.2
1975 56
1980 51.5
1990 46.6
1995 44.9

a) Find a function F(x) that models the percent of degrees that were earned by men. Let x represent the number of years after 1960.

a)Find a function F(x) that models the percent of degrees that were earned by women. Let x represent the number of years after 1960.

b)Use the functions found in parts (a) and (b) to determine when equal percent of men and women earned degrees.

I think if I can just find the first problem then I'll get the rest. Help?

 

[stapel]

What methods have they given you for finding equations? Are you supposed to do a regression on your calculator? Or something else?

Please be complete. Thank you!

 

[fasteddie65]

I plotted the points on my calculator and observed that the first data set is roughly linear. So I did a linear regression on both sets of data.

For the men, I found the equation y = -0.603x + 64.975.

For the women, I found the equation y = 0.603x + 35.025.

Then I found the intersection point: (24.84, 50)

So the percent of men will equal the percent of women in the year 1985.

 

[Denis]

Ah geezzzz, FastOne... :shock:

 

[Deleted member 4993]

An exponential fit of the nature:

y = A * e[sup:1b6zun6j]b*x[/sup:1b6zun6j]

Has a higher coefficient of determination (R[sup:1b6zun6j]2[/sup:1b6zun6j]) value than that of linear regression.

Moreover subject heading was "non-linear...."

 

[fasteddie65]

I guess I didn't read the problem carefully enough. Notice that my name is not "Careful Eddie".

The exponential equations turn out to be y ? 65.550 • 0.989^x and y ? 35.527 • 1.013^x.

The intersection turns out to be approximately (24.870, 49.698), which means the percents are the same when t ? 24.870, which would be in the year 2005, if the initial year is 1980. (I forget in which year the data began.)

 

[fasteddie65]

I just notice that the starting year is 1960, so the year in question is 1985. :|