Solve the problem.
-The revenue for a small company is given by the quadratic function $r ( t ) = 5 t ^ { 2 } + 5 t + 630$ where $t$ is the number of years since 1998 and $\mathrm { r } ( \mathrm { t } )$ is in thousands of dollars. If this trend continues, find the year after 1998 in which the company's revenue will be $\$ 730$ thousand. Round to the nearest whole year.
A) 2002
B) 2003
C) 2004
D) 2006

Question

Quizplus · Accepted Answer

The correct answer is A.To find the year in which the company's revenue will be $730 thousand, we need to solve the equation $r(t) = 730$.Substituting $r(t) = 5t^2 + 5t + 630$ into the equation, we get:$$5t^2 + 5t + 630 = 730$$Simplifying the equation, we get:$$5t^2 + 5t - 100 = 0$$Dividing both sides of the equation by 5, we get:$$t^2 + t - 20 = 0$$Factoring the equation, we get:$$(t - 4)(t + 5) = 0$$Setting each factor equal to zero, we get:$$t - 4 = 0 \quad \Rightarrow \quad t = 4$$$$t + 5 = 0 \quad \Rightarrow \quad t = -5$$Since $t$ represents the number of years since 1998, we can discard the negative solution. Therefore, the company's revenue will be $730 thousand in the year $1998 + 4 = 2002$.

Solve the Problem r(t)=5t2+5t+630r ( t ) = 5 t ^ { 2 } + 5 t + 630r(t)=5t2+5t+630

Solve the Problem $r ( t ) = 5 t ^ { 2 } + 5 t + 630$