The rate of growth of a population of micro-organisms is modelled by the equation: dP/dt = 3t^2+6t, where P is the population size at time t hours. Given that P=100 at t=1, find P in terms of t.
First, we integrate the equation with respect to t to find an equation for P. dP/dt = 3t2 + 6t Then, P= integral (3t2 + 6t) dt Integrating gives P= t3+3t2+c, c is the constant of integration. As we are given the boundary condition P=100 when t=1, sub in these values into the equation for P to find what c is. 100=13+3(12) +c Gives c=96 We get an equation for P with the correct value of c, P=t3+3t2+96
CB
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