Math Is Fun Forum

naowsek

Member

Registered: 2012-07-04

Posts: 1

Application of Differential Equations-Exponential Growth and Decay

Please can you help me to solve these questions?

Que 1.A bacterial culture is known to grow at a rate proportional to the amount present after one hour is 1000 strands of the bacteria are observed in the culture and after 4hrs,3000 strands.
Find:
a.An expression for the approximate number of strands of the bacterial present in the culture at anytime (T) .
b.The approximate number of strands originally in the culture.

Que 2.A certain radioactive material is known to decay at rate proportional to the amount present.If initially theres 50mg of the material present and after 2hrs it is observed that the material has lost 10 percent of its original mass find:

a.An expression for the the mass of the material remaining at anytime (T).
b.the mass of the material after 4hrs.
c.the time at which the material has has decayed to one half of its initial mass

Thanks,hoping to hear from you soon.

From Nana,Ghana.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,582

Re: Application of Differential Equations-Exponential Growth and Decay

hi naowsek

Welcome to the forum.

Q1.

where A is the Amount of bacteria and k is a constant.

Solve the differential equation and substitute the values to get k and the constant of integration.

then put t = 0

Bob

Q2,

Because this is decay, you can use a similar equation, but with a minus sign ... -kA

Bob

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