Answer
A) Since the rate of change is constant, life expectancy is linear.
B) $L =0.25 t+75.95$
C) Babies born in 2050 will have a life expectancy of about 88.35 years.
Work Step by Step
A) Since the rate of change is constant, life expectancy is linear.
B) The slope of the function is $m= \frac{3}{12}= 0.25$ per year. Let $L = b+mt$ the life expectancy function. When $t= 11$, $L= 78.7$. Thus
$$
\begin{aligned}
L-78.7 & =0.25(t-11) \\
L-78.7 & =0.25 t-2.75 \\
L & =0.25 t+75.95
\end{aligned}
$$
C) Set $t=50$, and find the value $L=0.25(50)+75.95=88.35$. Babies born in 2050 will have a life expectancy of about 88.35 years.
