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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.

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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

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