   Chapter 5, Problem 20RE ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Revenue A company produces a new product for which the rate of change of the revenue can be modeled by d R d t = 0.675 t 3 / 2 ,       0 ≤ t ≤ 225 where t is the time (in weeks). When t = 0, R = 0.(a) Find a model for the revenue function.(b) What is the revenue after 20 weeks?(c) When will the weekly revenue be $27,000? (a) To determine To calculate: The model function for the company which rate of change of the revenue can be modeled by dRdt=0.675t3/2. Explanation Given Information: The rate of change of the revenue; dR(t)dt=0.675t3/2,0t225. The initial condition R(0)=0 Here time (in weeks) is t. Formula used: The power rule of integrals: undu=un+1n+1+C (for n1) Here, u is function of x. The property of Intro-differential: df(x)dxdx=f(x) Calculation: Consider the derivative: dRdt=0.675t3/2 Apply, integration on both sides: dRdtdt=(0 (b) To determine To calculate: The revenue produced by company after 20 weeks. (c) To determine To calculate: The number of week when the weekly revenue be$27000.

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