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Let the population of rabbits surviving at a time t be governed by the differential equation `(d p(t))/(dt)=1/2p(t)-200.` If `p(0)""=""100` , then p(t) equals (1) `400-300""e^(t//2)` (2) `300-200""e^(-t//2)` (3) `600-500""e^(t//2)` (4) `40-300""e^(-t//2)`

A

`400-300e^(t/(2)`

B

`300-200e^(t/(2)`

C

`600-500e^(t/(2)`

D

`400-300e^(t/(2)`

Text Solution

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A
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ARIHANT MATHS ENGLISH-DIFFERENTIAL EQUATION -Exercise (Questions Asked In Previous 13 Years Exam)
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  2. A curve passes through the point (1,(pi)/(6)). Let the slope of the cu...

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  3. Let f:[0,1]rarrR (the set of all real numbers) be a function. Suppose ...

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  4. Let f:[0,1]rarrR be a function. Suppose the function f is twice differ...

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  5. Let f:[0,1]rarrR (the set of all real numbers) be a function. Suppose ...

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  6. Let f:[0,1]toR (the set of all real numbers ) be a function. Suppose t...

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  7. If y(x) satisfies the differential equation y^(prime)-ytanx=2xs e c...

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  8. Let y^(prime)(x)+y(x)g^(prime)(x)=g(x)g^(prime)(x),y(0),x in R , wher...

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  9. Let f: R to R be a continuous function which satisfies f(x)= int0^xf(...

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  10. Let a solution y=y(x) of the differential equation xsqrt(x^(2)-1) dy-...

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  11. If a curve y=f(x) passes through the point (1,-1) and satisfies the di...

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  12. Let y(x) be the solution of the differential equation (xlogx)(dy)/(dx)...

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  13. Let the population of rabbits surviving at a time t be governed by t...

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  14. At present, a firm is manufacturing 2000 items. It is estimated tha...

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  15. The population p(t) at time t of a certain mouse species satisfies the...

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  16. If (dy)/(dx)=y+3 and y(0)=2, then y(log2) is equal to

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  17. Let I be the purchase value of an equipment and V(t) be the value afte...

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  18. Solution of the differential equation cosxdy=y(sinx-y)dx, 0ltxlt(pi)...

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  19. The differential equation which represents the family of curves y=c(1)...

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  20. The differential equation of the family of circles with fixed radius ...

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