Differential Model Equations

 a. Compartmental Analysis

Question 18

Using the U.S. census data in Table 3.1 for 1900, 1920, and 1940 to determine parameters in the logistic equation model, what populations does the model predict for 2000 and 2010? Compare your answers with the census data for those years.

Question 9

In 1990 the Department of Natural Resources released 1000 splake (a crossbreed of fish) into a lake. In 1997 the population of splake in the lake was estimated to be 3000. Using the Malthusian law for population growth, estimate the population of splake in the lake in the year 2020.

b. Mathematical Models "Heating and Cooling" .
Question 2

A cold beer initially at 35oF warms up to 40oF in 3 min while sitting in a room of temperature 70oF. How warm will the beer be if left out for 20 min?

Question 6

On a mild Saturday morning while people are working inside, the furnace keeps the temperature inside the building at 21degrees C. At noon, the furnace is turned off, and the people go home. The temperature outside is a constant 12 degrees C for the rest of the afternoon. If the time constant for the building is 3 hr, when will the temperature inside the building reach 16 degrees C? If some windows are left open and the time constant drops to 2 hr, when will the temperature inside reach 16 degrees C?