A population PPP follows dPdt=0.02P\frac{dP}{dt} = 0.02PdtdP=0.02P. Find P(t)P(t)P(t) if P(0)=200P(0) = 200P(0)=200.
P(t)=200+0.02tP(t) = 200 + 0.02tP(t)=200+0.02t
P(t)=200e0.02tP(t) = 200e^{0.02t}P(t)=200e0.02t
P(t)=200e0.02P(t) = 200e^{0.02}P(t)=200e0.02
P(t)=0.02e200tP(t) = 0.02e^{200t}P(t)=0.02e200t