can anyone give an example of calculus in real time situation application?

Question

experimentx · Answer

Calculus real time application?? 
how do you know the area of circle is (pi)r^2
how do you know the volume of sphere is 4/3(pi)r^3
how would you know the mass of Earth???

anonymous · Answer

http://www.intmath.com/applications-integration/applications-integrals-intro.php does this site help?

kira_yamato · Answer

The population of a country is under study. It is known that the annual birth rate is equal to r times its population and annual death rate is equal to r/k times the square of its population, where r and k are positive constants. At time (in years) t = 0, the population of the country was N, where N < k. Let x(t) = population of the country after t years. Assume that x(t) is a continuous variable. 
(a) Set up a differential equation to relate the rate of population increase dx/dt to birth and death rates. By solving this differential equation, show the following relationship:
$$x(t) = \frac{kN}{N+(k-N)e^{-rt}}$$
(b) In 1996, the population of the country was 5 million and the rate of increase is 1.5%. Suppose r = 0.02, predict the population of the country in 2006.

kira_yamato · Answer

An infectious disease spreads at a rate which is proportional to the product of the number infected and the number uninfected. Initially, half the population is infected and the rate of spread is such that, were it to remain constant, the whole population will be infected in exactly 24 days. Calculate the proportion of population that is infected after 12 days. (Topic: Differential Eq'ns)

jamesj · Answer

I like Kira's example.  Seen the movie "Contagion"?  They use a one-paramater differential equation to predict how a new disease will spread.  In the movie the parameter is called r_0 "r zero" or "r nought".

jamesj · Answer

Also, I used calculus once as one of the tools to help a company figure out the optimal size for its sales force.  As a result, they hired about another 100 people.