A company started oil production in a given location at an initial production rate of

$1200$MT$/$day$.$ The production rate increased exponentially at an annual build$-$up

rate of $10\%$ for $8$ years. Estimate:

$($i$)$ The instantaneous build$-$up rate; $($ii$)$ The production rate at the peak of

production;

$($iii$)$ The PV$($production$)$ at a discount rate of $16\%.$