In the model of Exercise 12, let A(t) be the area at time t (hours) of a growing tissue culture with initial size A(0) = 1 cm², assuming that the maximum area is M = 16 cm² and the growth constant is k = 0.1.

(a) Find a formula for A(t). The initial condition is satisfied for two values of the constant c. Choose the value of C for which A(t) is increasing.

(b) Determine the area of the culture at t = 10 hours.

(c) Graph the solution using a graphing utility.

Data From Exercise 12

A tissue culture grows until it has a maximum area of M square centimeters. The area A(t) of the culture at time t may be modeled by the differential equation

where k is a growth constant.

Transcribed Image Text:

dA dt * = K √₁ (1 - A) k M