Question

The rate of change in sales S is inversely proportional to time t (t > 1), measured in weeks. Find S as a function of t when the sales after 2 and 4 weeks are 162 units and 287 units, respectively.

Answer 1

Answer:

S = 250/t

Step-by-step explanation:

If the rate of change of sales is inversely proportional to the time t, this is expressed mathematically as ΔS ∝ 1/Δt

ΔS = k/Δt where k is the constant of proportionality

If ΔS = S₂-S₁ and Δt = t₂-t₁

S₂-S₁ = k/ t₂-t₁

If the sales after 2 and 4 weeks are 162 units and 287 units respectively, then when S₁  = 162, t₁ = 2 and when   S₂ = 287, t₂ = 4.

On substituting this values into the given functions, we will have;

287 - 162 = k/4-2

125 = k/2

cross multiplying

k = 125* 2

k = 250

Substituting k = 250 into the function ΔS = k/Δt

ΔS = 250/Δt

S = 250/t

Hence the value of S as function of t when the sales after 2 and 4 weeks are 162 units and 287 units, respectively is expressed as S = 250/t