Question

Day	Number of coffee sold
3	21
4	35
5	53
6	75
7	101

The above data shows the number of coffee sold by the famous coffee shop at a particular venue. If the number is shown by $v$ and days as $t$, then they are related by

• A. $v\left(t\right)=2t^2+3$
• B. $v\left(t\right)=\frac{t^2}{2}+3$
• C. $v\left(t\right)=2t^2+21$
• D. $v\left(t\right)=\frac{t^2}{2}+21$

Answer 1

The correct option is A $v\left(t\right)=2t^2+3$

Since all the given options have a quadratic function as the dependence, we assume the dependence as $v\left(t\right)=a{t}^2+bt+c$, where $a,b,c$ are unknowns.

Since we have $5$ readings, we take into account the first three readings to get $a,b,c$.

$21=9a+3b+c...\left(1\right)$

$35=16a+4b+c...\left(2\right)$

$53=25a+5b+c...\left(3\right)$

Subtracting equations (1) and (2) gives $14=7a+b...\left(4\right)$

Subtracting equations (2) and (3) gives $18=9a+b...\left(5\right)$

Subtracting equations (4) and (5) gives $2a=4$ and so $a=2$

Substituting this in equation (4) gives $14=14+b$ or $b=0$

Substituting values of a and b in equation (1) gives $21=18+0+c,$ giving $c=3$

So, $v\left(t\right)=2t^2+3$