Question

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

Answer 1

1) 4.5% 2)1%

Explanation:

Given equation The monthly profits:
`f(t) = (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) = (0^2 + 9)/(0^2 + 2)`

⇒
`f(0) = (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)( (t^2 + 9)/(t^2 + 2))`

`\lim_(n \to \infty)( (2t)/(2t))=1`

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

Answer 2

- 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:

`\lim_(t \to \infty) ( t^(2)+9)/( t^(2) +2)= \\ = \lim_(t \to \infty) (2t)/(2t) = 1`
( or $1,000 )