Question

The weekly sale S (in thousands of units) for the t^th week after the introduction of the product in the market is given by S=(120t)/(t2+100). In which week would the sale (S) have been 6?

Answer 1

So,
t represents the week
now, for S=6
6= (120t) / (t² + 100)
6t² + 600 =120t
6t² -120t + 600=0
t=(120 +√ (120² -4 × 6 × 600)  )/ (2 × 6)
t=(120)/12
t=10
So, it will take 10 weeks to achieve a sale of 6 thousand units

Answer 2

The tenth week will have sales (S) equalling 6.

 

The weekly sales (S) can be expressed in terms of a quadratic equation with the variable as the week (t). The equation can be expressed as:

 

S = (120 x t) / (t^2 + 100)

 

Assuming the sales to be 6 during the week t, we can calculate t using the following equation:

 

0 = 6t^2 – (120 x t) + 600

 

Here, we have simply substituted S = 6. Further simplifying the equation:

 

0 = t^2 – 20t + 100

 

Solving the quadratic equation, we get the solution of the quadratic to be:

 

t = 10 weeks.