Answer:
1) 4.5% 2)1%
Step-by-step explanation:
Given equation The monthly profits: [tex]f(t) = \frac{t^2 + 9}{t^2 + 2}[/tex]
where t is in months after june 1st,2002
To find : The company's profits on June 1st, 2002
which means t=0
⇒ [tex]f(0) = \frac{0^2 + 9}{0^2 + 2}[/tex]
⇒ [tex]f(0) = \frac{9}{2}[/tex]
⇒ [tex]f(0) = 4.5[/tex]
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
[tex]\lim_{n \to \infty}( \frac{t^2 + 9}{t^2 + 2})[/tex]
[tex]\lim_{n \to \infty}( \frac{2t}{2t})=1[/tex]
The company's profits many years into the future = 1%
