In the year 1970, the averge male life

Question

In the year 1970, the averge male life exspectance in the united states was 67.1 years, and in the year 2010 it grew to 76.2 years let x represent the years and y f(x) represent the male life expectancy in the u.s.

Answer 1

x= number of years since 1970

for 2010, x = 40

76.2 = 67.1e^40r

76.2/67.1 = e^40r

take natural logs

ln(76.2/67.1) = 40r

r = annual rate of change of the life span

= ln(76.2/67.1)/40 = about .318% = .00318

y=f(x) = 67.1e^.00318x = expected life expectancy in the US

(ignoring a recent lowering of life expectancy due to the pandemic)