In one model of the changing population P(t) of a community, it is assumed that dP dt = dB dt − dD dt , where dB/dt and dD/dt are the birth and death rates, respectively. (a) Solve for P(t) if dB/dt = k1P and dD/dt = k2P. (Assume P(0) = P0.)

Step-by-step explanation:

This leads to:

Taking the integral of both sides

......(i)

When t=0, P(t)=

From (i),

Therefore:

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is