Solve the problem.
-The function $f ( t ) = - 0.14 t ^ { 2 } + 0.49 t + 31.3$ models a certain country's population in millions, ages 65 and older, where $t$ represents years after 2010 . The function $g ( t ) = 0.54 t ^ { 2 } + 11.84 t + 108.1$ models the total yearly cost of the government's health insurance program in billions of dollars, where t represents years after 2010. What does the function $\frac { g } { f }$ represent? Find $\left( \frac { g } { f } \right) ( 5 )$.
A) Cost per person in thousands of dollars. $5.98 thousand
B) Cost per person in thousands of dollars. $0.17 thousand
C) Cost per person in thousands of dollars. $0.21 thousand
D) Cost per person in thousands of dollars. $12.22 thousand

Question

Quizplus · Accepted Answer

The function $\frac{g}{f}$ represents the cost per person (in billions of dollars divided by millions of people, which simplifies to thousands of dollars per person). To find $\left(\frac{g}{f}\right)(5)$, substitute $t = 5$ into both $g(t)$ and $f(t)$, then divide $g(5)$ by $f(5)$.

Solve the Problem f(t)=−0.14t2+0.49t+31.3f ( t ) = - 0.14 t ^ { 2 } + 0.49 t + 31.3f(t)=−0.14t2+0.49t+31.3

Solve the Problem $f ( t ) = - 0.14 t ^ { 2 } + 0.49 t + 31.3$