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 =

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

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total amount of money that he should pay if he has not used his duty free exemption is $98

step-by-step explanation:

given a united states citizen returning to the states declares the following items at the customs office: 3 shirts at $8.50 each 2 dresses at $27.50 each 1 pair of gold cuff links at $17.50 per pair. we have to find how much he pay

cost of 3 shirts if one cost at $8.50 is

cost of 2 dresses if one cost at $27.50 is  

cost of 1 pair of gold cuff at $17.50

so, total amount of money that he should pay if he has not used his duty free exemption is   $25.5+$55+$17.50=$98