Question

the functions $f(x) = -2.9x + 287$ and $g(x) = 0.01x^2 - 4.9x + 370$ 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 $f(70)$.
b. find and interpret $g(70)$.
c. which function serves as a better model for the chance of surviving to age 70?

a. select the correct choice below and fill in the answer box(es) to complete your choice.
(simplify your answers.)
\\(\bigcirc\\) a. $f(70)=\square$, which means that the chance of a 60 - year - old surviving to the age of $\square$ is 70%.
\\(\bigcirc\\) b. $f(70)=\square$, which means that the chance of a 60 - year - old surviving to the age of 70 is $\square$%.

Explanation:

Step1: Substitute x=70 into f(x)

$f(70) = -2.9(70) + 287$

Step2: Calculate f(70)

$f(70) = -203 + 287 = 84$

Step3: Substitute x=70 into g(x)

$g(70) = 0.01(70)^2 - 4.9(70) + 370$

Step4: Calculate g(70)

$g(70) = 0.01(4900) - 343 + 370 = 49 - 343 + 370 = 76$

Step5: Compare to bar graph value

Bar graph value for age 70 is 85.

Answer:

a. B. $f(70)=84$, which means that the chance of a 60-year-old surviving to the age of 70 is $84\%$.
b. $g(70)=76$, which means that the chance of a 60-year-old surviving to the age of 70 is $76\%$.
c. The function $f(x)$ serves as a better model, since its value (84) is closer to the bar graph value of 85 than the value of $g(x)$ (76).