Answer to Question #213965 in Differential Equations for rare

Question

2.The population N(t) of a species of micro-organism in a laboratory setting at any time t is established to vary under the influence of a certain chemical at a rate given by dN/dt=t-2e^t show that N(t)=t-2e^t+c.hence if N(0)=400 determine the population when t=5

Answer 1

$\frac{dN}{dt}=1-2e^t.$

$N=\int(1-2e^t)dt=t-2e^t+C.$

$N(0)=400\to -2+C=400\to C=402.$

$N(5)=5-2e^5+402=110.$