Question

The revenue for a small company is given by the quadratic function r(t) = 5tsquared + 5t + 630 where t is the number of years since 1988 and r(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.

Answer 1

`r(t)=5t^2+5t+630`

for:

`\begin{gathered} r(t)=730 \\ 5t^2+5t+630=730 \\ so\colon \\ 5t^2+5t-100=0 \end{gathered}`

Divide both sides by 5:

`t^2+t-20=0`

Factor:

The factors of -20 which sum to 1, are -4 and 5 so:

`(t-4)(t+5)=0`

So:

`\begin{gathered} t=4 \\ or \\ t=-5 \end{gathered}`

Since a negative year wouldn't make any sense:

`t=4`

Therefore, the company revenue will be $730 for the year:

`1998+t=1998+4=2002`

Answer:

2002