QUESTION $1$

A firm's average cost function takes the form

$AC=11Q+a+\frac{5}{Q}$

And it is known that $MC=72$ when $Q=3.$

$($a$)$ Find the value of a$.$

$($b$)$ Find the value of $AC$ when $Q=5.$

$($c$)$ Given the revenue function is $66Q-13Q^2,$ find the profit function, $.$

$($d$)$ Calculate the maximum profit.

QUESTION $2$

Molly invested RM$500$ in an account earning $4\mathrm{.}5\%$ annual interest that is compounded

monthly.

$($a$)$ How much will be in the account after $3$ years?

$($b$)$ How long will it take for the amount to grow to RM$750?$

Lisa invested RM$200$ in an account earning $5\mathrm{.}75\%$ annual interest that is compounded

continuously. How long will it take the investment to grow to RM$350?$

QUESTION $3$

Find the minimum number of terms that must be taken from the sequence $3,5,7,9,$dots

so that the sum is at least $440.$

A person who buys an insurance policy pays an increasing premium every year; that is$,$

RM$1,000,$ RM$1,100,$ RM$1,200$ and so on$.$

$($a$)$ Write the formula for the $n^{th}$ year's premium.