The marginal monthly cost of maintaining a group of summer student intern at love.com is computed by:   Compute, to the nearest $100 , the total monthly cost of love.com increases the size of the student intern program from five students to seven students.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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The marginal monthly cost of maintaining a group of summer student intern at love.com is computed by:

 

Compute, to the nearest $100 , the total monthly cost of love.com increases the size of the
student intern program from five students to seven students.

The mathematical function displayed is:

\[ c(x) = \frac{1000(x+3)^2}{\left(8 + (x+3)^3\right)^\frac{3}{2}} \]

This function expresses \( c(x) \) as a quotient of two expressions. 

- The **numerator** is \( 1000(x+3)^2 \), indicating that the expression inside the parentheses \( (x+3) \) is squared and then multiplied by 1000.
  
- The **denominator** is \( \left(8 + (x+3)^3\right)^\frac{3}{2} \). Here, the expression \( (x+3) \) is cubed, added to 8, and then the sum is raised to the power of \( \frac{3}{2} \).

This type of function is often used in calculus and algebra to study behavior such as growth, decay, or other properties related to changes in \( x \).
Transcribed Image Text:The mathematical function displayed is: \[ c(x) = \frac{1000(x+3)^2}{\left(8 + (x+3)^3\right)^\frac{3}{2}} \] This function expresses \( c(x) \) as a quotient of two expressions. - The **numerator** is \( 1000(x+3)^2 \), indicating that the expression inside the parentheses \( (x+3) \) is squared and then multiplied by 1000. - The **denominator** is \( \left(8 + (x+3)^3\right)^\frac{3}{2} \). Here, the expression \( (x+3) \) is cubed, added to 8, and then the sum is raised to the power of \( \frac{3}{2} \). This type of function is often used in calculus and algebra to study behavior such as growth, decay, or other properties related to changes in \( x \).
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