Since the creation of a social program, the percent of persons 65 years and over with a family income below the poverty level has declined. The percent can be approximated by the function [tex]P(t) = 30.71 - 5.77 \ln t[/tex], where [tex]t[/tex] is the number of years since 1965.
Find the percent of persons 65 and over with a family income below the poverty level and the rate of change in 1970.
Note: To find the percent, substitute [tex]t = 5[/tex] into the function [tex]P(t)[/tex] (since 1970 is 5 years after 1965). To find the rate of change, take the derivative of [tex]P(t)[/tex] with respect to [tex]t[/tex] and evaluate it at [tex]t = 5[/tex].
Answer (3)
actually rate means anything divided by time......hope it helps
To find the percent of persons 65 and over with income below the poverty level in 1970, substitute t = 5 into the function P(t). For the rate of change, calculate the derivative of the function, P'(t), and evaluate at t = 5 to obtain the rate of change for the year 1970. ;
In 1970, approximately 21.44% of persons aged 65 and over had a family income below the poverty level. The rate of decline of this percentage was about 1.154% per year. This indicates that fewer seniors were living below the poverty line compared to earlier years.
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