Answer
a) 25%
b) 10%
c) function $f$ is better
Work Step by Step
(a)
Put the value $x=90$ in the function to obtain the value as follows:
$\begin{align}
& f\left( 90 \right)=-2.9\times 90+286 \\
& =-261+286 \\
& =25
\end{align}$
Thus, $f\left( 90 \right)=25$
This implies that the chance of a 60-year old surviving to an age of 90 is 25%.
(b)
So, putting the value $x=90$ in the function g, we obtain:
$\begin{align}
& g\left( 90 \right)=0.01\times {{\left( 90 \right)}^{2}}-4.9\times 90+370 \\
& =0.01\times 8100-441+370 \\
& =81-71 \\
& =10
\end{align}$
Thus, $g\left( 90 \right)=10$
This implies that the chance of a 60-year old surviving to an age of 90 is 10%.
(c)
It can be seen from the graph that the chance of living to an age of 90 is 24%. $f\left( 90 \right)$ is closer to this value and therefore, that will be the answer.
Thus, function f serves as a better model for the chance of surviving to age 90.
