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.

a. Write down the differential equation the mass of the bacteria, m, satisfies:

b. Find the general solution of this equation. Use A as a constant of integration.

c. Which particular solution matches the additional information? m (t) =

d. What was the mass of the bacteria at time t=0? mass =

Question

Mathematics

Pierre Washington

13 February, 14:59

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.

a. Write down the differential equation the mass of the bacteria, m, satisfies:

b. Find the general solution of this equation. Use A as a constant of integration.

c. Which particular solution matches the additional information? m (t) =

d. What was the mass of the bacteria at time t=0? mass =

+4

Answers (1)

Know the Answer?

Madalyn Houston · Answer 1

a) dm/dt = 0.2m

b) ln (m) = 0.2t + A

c) ln (m) = 0.2t + ln (20) - 0.6

d) 11 grams

Step-by-step explanation:

a) dm/dt = 0.2m

b) dm/m = 0.2dt

ln (m) = 0.2t + A

c) At t = 3, dm/dt = 4

dm/dt = 0.2m

4 = 0.2m

m = 4/0.2 = 20

So, when t = 3, m = 20

ln (20) = 0.2 (3) + A

A = ln (20) - 0.6

ln (m) = 0.2t + ln (20) - 0.6

d) find m when t=0

ln (m) = 0.2 (0) + ln (20) - 0.6

ln (m) = ln (20) - 0.6

ln (m) = 2.3957322736

m = e^2.3957322736

m = 10.9762327224

m = 11