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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.



Answer :

[tex]r(t)=5t^2+5t+630[/tex]

for:

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

Divide both sides by 5:

[tex]t^2+t-20=0[/tex]

Factor:

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

[tex](t-4)(t+5)=0[/tex]

So:

[tex]\begin{gathered} t=4 \\ or \\ t=-5 \end{gathered}[/tex]

Since a negative year wouldn't make any sense:

[tex]t=4[/tex]

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

[tex]1998+t=1998+4=2002[/tex]

Answer:

2002

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