Question

Let the population of a species of birds surviving at a time \(t\) be governed by the differential equation \[ \frac{dp}{dt}-p=-100 \] If \(p(0)=50\), then \(p(-\ln2)\) is equal to:

• A. \(90\)
• B. \(40\)
• C. \(75\)
• D. \(100\)

Hint:

For linear differential equations: \[ \frac{dy}{dx}+Py=Q \] always use: \[ I.F.=e^{\int Pdx} \] Then convert the left side into an exact derivative.

Answer 1

The Correct Option is C