A colony of yeast cells grows according to the differential equation where is the…

MATHEMATICS · Multi-part · AP · Calculus AB · Differential Equations · Differential Equations

Problem

A colony of yeast cells grows according to the differential equation

\frac{dy}{dt}=0.28y,

where

y

is the number of cells and

t

is measured in hours. A biologist records the initial population at time

t=0

to be

y(0)=420

. Answer the following questions concerning this model of yeast growth. (a) Explain, without performing any calculations, why the solution

y(t)

to the differential equation is an increasing function on

t>0

. Support your answer by referencing features of the differential equation. (b) Describe the practical meaning of the parameter

0.28

in the context of this scenario, including appropriate units. (c) At time

t=5

hours, the expression

\dfrac{y(5)}{y(0)}

is calculated. Explain what this ratio represents in everyday language and how its numerical value could be interpreted by the biologist.