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
Related Maths A Level answers
All answers ▸Differentiate the following equation: f(x) = 5x^3 + 6x^2 - 12x + 4
Integrate ln(x)
Differentiate with respect to x: y=(6x^2-1)/2sqrt(x)
A and B have coordinates (2,3) and (5,15), respectively. Together they form line l. Find the equation for the line r that goes through C(7,-2) and is perpendicular to l. Give the answer in the format of y=mx+b