APFIVE Population Growth from a Rate Function
The instantaneous growth rate of a population is modeled by the equation $$\frac{dP}{dt}=50+5t$$. If the initial population at time $$t=0$$ is $$P(0)=1000$$, which of the following expressions correctly calculates the population size at $$t=6$$ years?
A
$$P(6)=1000+\int_0^6 (50+5*t)\,dt = 1000+(300+90)=1390$$
B
$$P(6)=1000*\int_0^6 (50+5*t)\,dt$$
C
$$P(6)=1000+6*(50+5*6)$$
D
$$P(6)=\int_0^6 (50+5*t)\,dt = 390$$
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