Use this same window to solve Question $4($c$)($v$)$ and $($vi$).$

Marks$]$

Question $1[20$ marks$]$

$($a$)$ Jacob Mandevu gets a job with a salary of $K160,000$ a year. He is promised an annual increment of $K2,000$ for each subsequent year. Find his total earnings for a $10-$year period.

$[4$ Marks$]$

$($b$)$ The demand function for calculators in a certain college in Kitwe is given by $P=190-0\mathrm{.}05Q.$

$($i$)$ Derive expressions for ${}_d$ in terms of $P$ only.

$[3$ Marks$]$

$($ii$)$ Calculate the value of ${}_d$ when $P=K120.$

$[3$ Marks$]$

$($iii$)$ Determine the number of calculators demanded when ${}_d=-1.$

$[3$ Marks$]$

$($Iv$)$ Explain the difference between the slope of a demand function and the price elasticity of demand.

$[2$ Marks$]$

$($c$)$ Solve the following equation: $lo{g}_2(x+1)+lo{g}_2(2x-1)=lo{g}_{2}x.$

$[5$ Marks$]$