Answer
a) 83%
b) 76%
c) f is better
Work Step by Step
(a)
We put $x=70$ in the function f to get the value as follows:
$\begin{align}
& f\left( 70 \right)=-2.9\times 70+286 \\
& =-203+286 \\
& =83
\end{align}$
Thus, $f\left( 70 \right)=83$
This implies that the chance of a 60-year old to survive to an age of 70 is $83\%$.
(b)
Put the value $x=70$ in the function g to get the value as follows:
$\begin{align}
& g\left( 70 \right)=0.01\times {{\left( 70 \right)}^{2}}-4.9\times 70+370 \\
& =0.01\times 4900-343+370 \\
& =49+27 \\
& =76
\end{align}$
Thus, $g\left( 70 \right)=76$.
This implies that the chance of a 60-year old to survive to age 70 is 76%.
(c)
From the graph it can be seen that the chance to live to an age of 70 is 86%.
$f\left( 70 \right)$ is closer to this value, and therefore, that should be the answer.
Thus, function f serves as a better model for the chance of surviving to age 70.
