Question

(1 point) according to one mathematical model, the average life expectancy for american men born in 1900 was 55 years. life expectancy has increased by about 0.2 years for each birth - year after 1900.
a) write an equation to model the problem. let ( l ) be the average life expectancy and let ( t ) represent the number of years after 1900. for example, ( t = 12 ) would represent the year 1912. you must include ( l=) in your answer.
answer:

b) if this trend continues, for which birth - year will the average life expectancy be 71 years? (note: you are asked for a year, not a value for ( t ))
in the year the average life expectancy was 71.

note: you can earn partial credit on this problem.

you have attempted this problem 0 times.
you have unlimited attempts remaining.

email instructor

Explanation:

Step1: Determine the linear - equation form

The general form of a linear equation is $L = mt + b$, where $m$ is the slope and $b$ is the y - intercept. Here, the initial life expectancy in 1900 ($t = 0$) is $b=55$ years and the rate of increase (slope) $m = 0.2$ years per year. So the equation is $L=0.2t + 55$.

Step2: Solve for $t$ when $L = 71$

Substitute $L = 71$ into the equation $L=0.2t + 55$.
$71=0.2t + 55$.
Subtract 55 from both sides: $71 - 55=0.2t$, so $16 = 0.2t$.
Divide both sides by 0.2: $t=\frac{16}{0.2}=80$.

Step3: Find the year

Since $t$ is the number of years after 1900, the year is $1900 + t$. Substituting $t = 80$, the year is $1900+80 = 1980$.

Answer:

a) $L = 0.2t+55$
b) 1980