   Chapter 11.3, Problem 84E Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

Bus Travel Thoroughbred Bus Company finds that its monthly costs for one particular year were given by C ( t ) = 100 + t 2 dollars after t months. After t months the company had P ( t ) = 1 , 000 + t 2 passengersper month. How fast is its cost per passenger changing after 6 months? [HINT: See Example 4(b).]

To determine

To calculate: The rate by which cost of Bus Company increases per person after 6 months such that monthly cost for one particular year is given by C(t)=100+t2 dollars per month and number of passengers is given by P(t)=1,000+t2 passengers per month.

Explanation

Given Information:

The monthly cost for one particular year is given by C(t)=10,000+t2 dollars per month and number of passengers is given by P(t)=1,000+t2 passengers per month.

Formula used:

1) Quotient rule of derivative of differentiable functions, f(x) and g(x) is,

ddx[f(x)g(x)]=f'(x)g(x)f(x)g'(x)[g(x)]2

Where, g(x)0.

2) Derivative of function using power rule,

y=xn is dydx=nxn1.

3)Derivative of a constant is 0.

4) Sum rule of derivative is

ddx[f(x)+g(x)]=ddx[f(x)]+ddx[g(x)]

Where, f(x) and g(x) are any two differentiable functions.

5) Constant multiple rule of derivative of function f(x) is

ddx[cf(x)]=cddx[f(x)]

Where, c is constant.

Calculation:

Consider the functions, C(t)=100+t2 and P(t)=1,000+t2

As, cost per passenger Q(t)=C(t)P(t).

So,

Q(t)=100+t21,000+t2

Calculate the derivative of the function Q(t) with respect to t

Apply Quotient rule,

Q'(t)=ddt(100+t2)(1,000+t2)(100+t2)ddt(1,000+t2)

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