$2.$ A company decides to change its floor plan from cubicle to open office. This will bring in a constant stream of $\backslash (\backslash$$ $1,000\backslash )$ in extra income annually. If the company invests this extra income in an account that earns $\backslash (4\mathrm{.}5\backslash \%\backslash )$ continuously compounded interest for ten years, is it worth the change? The change in floor plan costs $\backslash (\backslash$$ $9,500\backslash ).$

$($a$)$ Find the present value of the income stream.

$($b$)$ Based on the present value of the floor plan change, should the company proceed with the change? Why? $($Hint: Compare the present value of the income stream to the cost of the floor change$)$