Mylo O'Moore

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$T\left(x\right)=5000\mathrm{log}(x+1)$ .

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

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$T\left(x\right)=5000\mathrm{log}(x+1)$

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)$T\left(x\right)=5000\mathrm{log}(x+1)$

Replace x with$5000,T\left(5000\right)=5000\mathrm{log}(5000+1)$

Since$\mathrm{log}x={\mathrm{log}}_{10}x,T\left(5000\right)=5000{\mathrm{log}}_{10}5001$

Using calculator,$T\left(5000\right)\approx 5000\times 3.699$

$T\left(5000\right)\approx \mathrm{\$}18495}$

Based on this model, the total sales of the Northwest Creations resulting from 5000 catalogues is $18495

b)$T\left(x\right)=5000\mathrm{log}(x+1)$

Replace x with$24000,T\left(24000\right)=5000\mathrm{log}(24000+1)$

Since$\mathrm{log}x={\mathrm{log}}_{10}x,T\left(24000\right)=5000{\mathrm{log}}_{10}24001$

Using calculator,$T\left(24000\right)\approx 5000\times 4.3802$

$T\left(24000\right)\approx \mathrm{\$}21901}$

Based on this model, the total sales of the Northwest Creations resulting from the distribution of 24000 catalogues is $21901

c)$T\left(x\right)=5000\mathrm{log}(x+1)$

Replace x with$49000,T\left(49000\right)=5000\mathrm{log}(49000+1)$

Since$\mathrm{log}x={\mathrm{log}}_{10}x$ , we have $T\left(49000\right)=5000{\mathrm{log}}_{10}49001$

Using calculator,$T\left(49000\right)\approx 5000\times 4.6902$

$T\left(49000\right)\approx \mathrm{\$}23451}$

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.

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

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)

Replace x with

Since

Using calculator,

Based on this model, the total sales of the Northwest Creations resulting from 5000 catalogues is $18495

b)

Replace x with

Since

Using calculator,

Based on this model, the total sales of the Northwest Creations resulting from the distribution of 24000 catalogues is $21901

c)

Replace x with

Since

Using calculator,

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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