A colony of bacteria is growing at a rate of 0.2 times its mass. Here time is measured in hours and mass in grams. The mass of the bacteria is growing at a rate of 4 grams per hour after 3 hours.
Write down the differential equation the mass of the bacteria, m, satisfies: ′= .2m
Find the general solution of this equation. Use A as a constant of integration.
() = Ae^(.2t)
Which particular solution matches the additional information? () =
What was the mass of the bacteria at time =0? mass =

Explanation:

Question 1: Write down the differential equation the mass of the bacteria, m, satisfies: m′= .2m

a) By definition:  

b)  Given:  

c) By substitution:  

Question 2: Find the general solution of this equation. Use A as a constant of integration.

a) Separate variables

b) Integrate

c) Antilogarithm

Question 3. Which particular solution matches the additional information?

Use the measured rate of 4 grams per hour after 3 hours

First, find the mass at t = 3 hours

Now substitute in the general solution of the differential equation, to find A:

Round A to 1 significant figure:

Particular solution:

Question 4. What was the mass of the bacteria at time =0?

Substitute t = 0 in the equation of the particular solution:

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step-by-step explanation:

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