The functions $f(x)=-2.8 x+286$ and $g(x)=0.01 x^{2}-5.1 x+370$ model the chance, as a percent, that a 60 -year-old will survive to age $x$. The bar graph to the right shows the chances of 60 -year-olds surviving to various ages. a. Find and interpret $\mathrm{f}(70)$. b. Find and interpret $g(70)$. c. Which function serves as a better model for the chance of surviving to age 70 ?

Step 1 ：Substitute \(x = 70\) into the function \(f(x) = -2.8x + 286\) to find \(f(70)\)

Step 2 ：Calculate \(f(70) = -2.8(70) + 286 = -196 + 286 = 90\)

Step 3 ：\(\boxed{f(70) = 90}\) is the interpretation that according to the linear model \(f(x)\), there is a 90% chance that a 60-year-old will survive to age 70

Step 4 ：Substitute \(x = 70\) into the function \(g(x) = 0.01x^2 - 5.1x + 370\) to find \(g(70)\)

Step 5 ：Calculate \(g(70) = 0.01(70)^2 - 5.1(70) + 370 = 49 - 357 + 370 = 62\)

Step 6 ：\(\boxed{g(70) = 62}\) is the interpretation that according to the quadratic model \(g(x)\), there is a 62% chance that a 60-year-old will survive to age 70

Step 7 ：The function that serves as a better model for the chance of surviving to age 70 is the one that gives a result closer to the actual survival rate for 70-year-olds. Without knowing the actual survival rate, we cannot definitively say which function is a better model. However, if we assume that the actual survival rate is somewhere between the two predictions, then the function \(f(x)\) would be a better model as it gives a higher survival rate of 90% compared to the 62% predicted by \(g(x)\)