Calculate Future Sales of Calculus and You Text

  • Thread starter Thread starter MathNoob123
  • Start date Start date
  • Tags Tags
    Integrals
Click For Summary
SUMMARY

The discussion focuses on calculating the future sales of the textbook "Calculus and You," which is experiencing a continuous decline of 4% per year from an initial sales figure of 4,800 copies annually. The correct approach to model this decline involves using the exponential decay formula, specifically exp(-0.04*t), rather than the previously attempted integral formulations. The user initially set up the integral incorrectly, leading to inaccurate results. The correct integral setup should reflect the continuous nature of the decline in sales.

PREREQUISITES
  • Understanding of exponential decay functions
  • Familiarity with integral calculus
  • Knowledge of limits in calculus
  • Ability to apply mathematical modeling to real-world scenarios
NEXT STEPS
  • Study the properties of exponential functions and their applications in modeling decay
  • Learn how to set up and evaluate improper integrals
  • Explore the concept of limits in calculus, particularly in the context of infinity
  • Practice problems involving continuous growth and decay models
USEFUL FOR

Students in calculus courses, educators teaching mathematical modeling, and anyone interested in applying calculus to real-world sales forecasting scenarios.

MathNoob123
Messages
15
Reaction score
0

Homework Statement


Sales of the text Calculus and You have been declining continuously at a rate of 4% per year. Assuming that Calculus and You currently sells 4800 copies per year and that sales will continue this pattern of decline, calculate total future sales of the text.


Homework Equations


integral of a to infinity f(x)dx=lm of M>>infinity of integral of a to M f(x)dx


The Attempt at a Solution



I set the problem as integral of 0 to M 4800(0.96)^t dt and computed it, but my answer was incorrect. So then I did the opposite by setting the integral from M to 0, but my answer was still incorrect. Any help would be appreciated. Arigato Gozaimasu!
 
Physics news on Phys.org
Your formula for 'declining continuously at a rate of 4% per year' is a bit wrong. Don't you want exp(-0.04*t)?
 

Similar threads

Calculate this Integral around the Circular Path using Green's Theorem
  • · Replies 3 ·
Replies
3
Views
2K
Finding Area of Shaded Segment in Circle Using Calculus
  • · Replies 6 ·
Replies
6
Views
2K
Help me prove integral answer over infinitesimal interval
  • · Replies 9 ·
Replies
9
Views
2K
Uniform convergence of a parameter-dependent integral
  • · Replies 6 ·
Replies
6
Views
2K
Improper integral with spherical coordinates
  • · Replies 1 ·
Replies
1
Views
2K
Difficult Vector Field Integral
  • · Replies 3 ·
Replies
3
Views
1K
Find Fourier coefficients - M. Chester text
  • · Replies 4 ·
Replies
4
Views
2K
Determine the truth of the following statements
  • · Replies 3 ·
Replies
3
Views
1K
The integral of a function ##f(x)## from its graph
  • · Replies 15 ·
Replies
15
Views
2K
Undergrad Should the function f to be continuous for applying MVTI or not?
  • · Replies 4 ·
Replies
4
Views
1K