To find: The total sales T(x) of Northwest Creations, to the

Mylo O'Moore

Mylo O'Moore

Answered question

2021-08-19

To find:
The total sales T(x) of Northwest Creations, to the nearest dollar using the model where the distribution of x thousand catalogues is approximated by T(x)=5000log(x+1).

Answer & Explanation

Fatema Sutton

Fatema Sutton

Skilled2021-08-20Added 88 answers

Concept:
Modeling is a method of simulating the real life situations with mathematical equations. Using these models we can forecast the future behavior. We can translate the mathematical word problem into a math expression using variables.
Calculation:
The given model is T(x)=5000log(x+1)
Where x is the number of catalogues distributed in throusands and T(x) is the total sales in dollars.
So, in order to get the total sales T(x), replace x in the given model with the number of catalogues.
a) T(x)=5000log(x+1)
Replace x with 5000,T(5000)=5000log(5000+1)
Since logx=log10x,T(5000)=5000log105001
Using calculator, T(5000)5000×3.699
T(5000)$18495
Based on this model, the total sales of the Northwest Creations resulting from 5000 catalogues is $18495
b) T(x)=5000log(x+1)
Replace x with 24000,T(24000)=5000log(24000+1)
Since logx=log10x,T(24000)=5000log1024001
Using calculator, T(24000)5000×4.3802
T(24000)$21901
Based on this model, the total sales of the Northwest Creations resulting from the distribution of 24000 catalogues is $21901
c) T(x)=5000log(x+1)
Replace x with 49000,T(49000)=5000log(49000+1)
Since logx=log10x, we have T(49000)=5000log1049001
Using calculator, T(49000)5000×4.6902
T(49000)$23451
Based on this model, the total sales of the Northwest Creations resulting from 49000 catalogues is $23451
Final statement:
Based on this model, the total sales of the Northwest Creations resulting from 5000 catalogues is $18495, from 24000 catalogues is $21901 and from 49000 catalogues is $23451.

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