(a) (i) The trick here is to recognize that you need to divide r by 100 and then add 1 to it.

(a) (ii) similar to the last question, multiply the result from (i) by (1+r/100) and then minus 300000

or

of course here we reject the negative answer for r since it can’t be negative and hence we have

(b) (i)

After 1st year, Area

After 2nd year, Area

After 3rd year, Area

After nth year, Area

(b) (ii)

Since n is an integer therefore . At the end of 21st year

(c)

Setup the system of equations by the given information in the table,

Assume the claim is true, which means,

Now we need to show the RHS is greater than zero to get the contradiction and there are two ways in doing so.

*Method 1 (Using Determinant)*

and since the leading coefficient of is positive, therefore

Therefore contradiction and the claim is false.

*Method 2 (Using Completing the Square)*

Again, contradiction, hence the claim is false.