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1. Use intergration to solve the differential equation:

dx/dt = -1/40(x-15) , x>15

given that x=85 when t=0, expressing t in terms of x.

2. A disease is spreading through a colony of rabbits. There are 5000 rabbits in the colony. At the time t hours, x is the number of rabbits infected. The rate of increase of the number of rabbits infected is proportional to the product of the number of rabbits infected and the number not yet infected.

Formulate a differential equation for dx/dt in terms of variables x and t and a constant of proportionality k.

Thank you!!

dx/dt = -1/40(x-15) , x>15

given that x=85 when t=0, expressing t in terms of x.

2. A disease is spreading through a colony of rabbits. There are 5000 rabbits in the colony. At the time t hours, x is the number of rabbits infected. The rate of increase of the number of rabbits infected is proportional to the product of the number of rabbits infected and the number not yet infected.

Formulate a differential equation for dx/dt in terms of variables x and t and a constant of proportionality k.

Thank you!!

1) Separate the variables.

2) Just change the words to maths.

The rate of increase of the number of rabbits infected

dx/dt

is proportional to

= k*

the product of the number of rabbits infected and the number not yet infected.

x*(5000-x).

(edited 13 years ago)

Original post by Jonnislats

1. Use intergration to solve the differential equation:

dx/dt = -1/40(x-15) , x>15

given that x=85 when t=0, expressing t in terms of x.

2. A disease is spreading through a colony of rabbits. There are 5000 rabbits in the colony. At the time t hours, x is the number of rabbits infected. The rate of increase of the number of rabbits infected is proportional to the product of the number of rabbits infected and the number not yet infected.

Formulate a differential equation for dx/dt in terms of variables x and t and a constant of proportionality k.

Thank you!!

dx/dt = -1/40(x-15) , x>15

given that x=85 when t=0, expressing t in terms of x.

2. A disease is spreading through a colony of rabbits. There are 5000 rabbits in the colony. At the time t hours, x is the number of rabbits infected. The rate of increase of the number of rabbits infected is proportional to the product of the number of rabbits infected and the number not yet infected.

Formulate a differential equation for dx/dt in terms of variables x and t and a constant of proportionality k.

Thank you!!

Did you get the answer to the first question ?

Original post by RahulMathew

Did you get the answer to the first question ?

This thread is 10 years old and that poster hasn't been active since 2011 so I suspect if they did get an answer it has now drifted out of their consciousness

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- Differentiation
- AS-Level Maths Questions.
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- AS Maths Exponential Question
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- Intergrate
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- Edexcel A-level Mathematics Paper 1 [6th June 2023] Unofficial Markscheme
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