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The population P in any year t is such ...

The population P in any year t is such that the rate of increase in the population is proportional to the population. Then

A

`P = ce^(kt)`

B

`P = ce^(-kt)`

C

`P = ckt`

D

`P=c`

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The correct Answer is:
A
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PREMIERS PUBLISHERS-ORDINARY DIFFERENTIAL EQUATIONS -SOLUTION TO EXERCISE 10.9
  1. The general solution of the differential equation (dy)/(dx)=(y)/(x) is

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  2. The solution of the differential equation 2x(dy)/(dx)-y=3 represents

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  3. The solution of (dy)/(dx)+p(x)y=0 is

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  4. The integrating factor of the differential equation (dy)/(dx)+y=(1+y)/...

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  5. The integrating factor of the differential equation (dy)/(dx)+P(x)y=Q(...

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  6. The degree of the differential equation y(x)=1+(dy)/(dx)+(1)/(1.2)((dy...

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  7. If p and q are the oder and degree of the differential equation y(dy)/...

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  8. The solution of the differential equation (dy)/(dx)+(1)/(sqrt(1-x^(2))...

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  9. The solution of the differential equation (dy)/(dx)=2xy is

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  10. The general solution of the differential equation log((dy)/(dx))=x+y i...

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  11. The solution of (dy)/(dx)=2^(y-x) is

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  12. The solution of the differential equation (dy)/(dx)=(y)/(x)+(phi((y)/(...

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  13. If sinx is the integrating factor of the linear differential equation ...

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  14. The number of arbitrary constants in the general solutions of order n ...

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  15. The number of arbitrary constants in the particular solution of a diff...

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  16. Integrating factor of the differential equation is (dy)/(dx)=(x+y+1)/(...

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  17. The population P in any year t is such that the rate of increase in t...

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  18. P is the amount of certain substanc left in after time t. If the rate ...

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  19. If the solution of the differential equation (dy)/(dx) = (ax+3)/(2y+f...

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  20. The slope at any point of a curve y=f(x) is given by (dy)/(dx)=3x^(2) ...

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