Question

the functions f(x)= - 2.8x + 287 and g(x)=0.01x² - 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?
select the correct choice below and fill in the answer box(es) to complete your choice.
a. f(70)=94 which means that the chance of a 60 - year - old surviving to the age of 70 is 94%
b. f(70)=, which means that the chance of a 60 - year - old surviving to the age of 70 is %

Explanation:

Step1: Evaluate f(70)

Given \(f(x)= - 2.8x + 287\), substitute \(x = 70\).
\[

$$\begin{align*} f(70)&=-2.8\times70 + 287\\ &=-196+287\\ &=91 \end{align*}$$

\]

Step2: Evaluate g(70)

Given \(g(x)=0.01x^{2}-4.9x + 370\), substitute \(x = 70\).
\[

$$\begin{align*} g(70)&=0.01\times70^{2}-4.9\times70 + 370\\ &=0.01\times4900-343 + 370\\ &=49-343+370\\ &=76 \end{align*}$$

\]
From the bar - graph, the chance of a 60 - year - old surviving to age 70 is 94. Since the value from the bar - graph is 94, and \(f(70)=91\), \(g(70)=76\), the function \(f(x)\) is a better model as its value 91 is closer to 94.

Answer:

A. \(f(70)=91\) which means that the chance of a 60 - year - old surviving to the age of 70 is 91%.
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 for the chance of surviving to age 70.