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A once thriving company in Teaneck had its monthly profits, in thousands of dollars, modeled by the equation?

f(t) = t^2 + 9/ 1t^2 + 2


where t is in months after June 1st, 2002.


Estimate the company's profits on June 1st, 2002.

Estimate the company's profits many years into the future

Verified Answer :

HomertheGenius
  • The company`s profits on June 1st, 2002:
    t = 0
    f ( 0 ) = ( 0² + 9 ) / ( 0² + 2 ) = 9/2 = 4.5 ( or $4,500 )
    - The company`s profits many years into the future:
    @@MATH_TOKEN_0@@
    ( or  $1,000 )

Answer:

1) 4.5%    2)1%

Step-by-step explanation:

Given equation The monthly profits: \(f(t) = \frac{t^2 + 9}{t^2 + 2}\)

where t is in months after june 1st,2002

To find : The company's profits on June 1st, 2002

which means t=0

⇒ \(f(0) = \frac{0^2 + 9}{0^2 + 2}\)

⇒ \(f(0) = \frac{9}{2}\)

⇒ \(f(0) = 4.5\)  

The company's profits on June 1st, 2002 = 4.5%

To find :The company's profits many years into the future

we take limit tends to infinity

\(\lim_{n \to \infty}( \frac{t^2 + 9}{t^2 + 2})\)

\(\lim_{n \to \infty}( \frac{2t}{2t})=1\)

The company's profits many years into the future = 1%


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