Answer:
S = 250/t
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