A population grows according to dPdt=0.05P\frac{dP}{dt} = 0.05PdtdP=0.05P. If P(0)=100P(0) = 100P(0)=100, what is P(t)P(t)P(t)?
P(t)=100e0.05tP(t) = 100e^{0.05t}P(t)=100e0.05t
P(t)=100+0.05tP(t) = 100 + 0.05tP(t)=100+0.05t
P(t)=100e0.5tP(t) = 100e^{0.5t}P(t)=100e0.5t
P(t)=5t+100P(t) = 5t + 100P(t)=5t+100