Total sales of a fad product S may increase slowly at first while the product is relatively unknown, more rapidly as its popularity rises, and then level of toward a ;og term maximum as consumers mive onto another product. Consider the model In(1-S)-In(S) kt +C, where S is the fraction of total sales (S 1 means 100%), t weeks after the product is introduced, and k and C are constants. Solve the model for sales S in terms of k, t, and C.

Sales, S(t)= 1/(Ceᵏᵗ+1)

Step-by-step explanation:

In(1-S)-In(S) = kt +C

Applying Laws of Logarithm

ln A- ln B= ln (A/B)

In(1-S)-In(S) = kt +C

ln ((1-S)/S) =kt + C

Taking the exponential of both sides

(1-S)/S = eᵏᵗ⁺ᶜ

(1-S)/S = eᵏᵗ*eᶜ

Now, exponential of a constant,

eᶜ = C where C is an arbitrary constant.

(1-S)/S = Ceᵏᵗ

1-S= SCeᵏᵗ

SCeᵏᵗ +S=1

S(Ceᵏᵗ+1)=1

S(t)= 1/(Ceᵏᵗ+1)

its 69.420

step-by-step explanation:

an advantage of the standard deviation is that it increases as the dispersion of the data increases. e. the interquartile range is preferred when the data are not skewed or no have outliers. an advantage of the standard deviation is that it uses all the observations in its computation.