A mathematical model for the area A (in cm2) that a colony

Chapter 9, Problem 14E

(choose chapter or problem)

A mathematical model for the area A (in \(\mathrm{cm}^{2}\)) that a colony of bacteria (B. dendroides) occupies is given by

\(\frac{d A}{d t}=A(2.128-0.0432 A)\). *

Suppose that the initial area is 0.24 \(\mathrm{cm}^{2}\).

(a) Use the RK4 method with h  0.5 to complete the following table:

(b) Use a numerical solver to graph the solution of the initial-value problem. Estimate the values A(1), A(2), A(3), A(4), and A(5) from the graph.

(c) Use separation of variables to solve the initial-value problem and compute the actual values A(1), A(2), A(3), A(4), and A(5).

Text Transcription:

mathrm cm^2