# Chapter 1 - Section 1.2 - Basics of Functions and Their Graphs - Exercise Set - Page 179: 102

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.

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