Math Help - Integration (population growth)

1. Integration (population growth)

A population of bacteria is changing at a rate of

dP/dt = 3000/(1+0.25t)

where t is the time in days. The initial population (when t=0) is 1000. Write an equation that gives the population at any time t, and find the population when t=3 days.

2. Originally Posted by saiyanmx89
A population of bacteria is changing at a rate of

dP/dt = 3000/(1+0.25t)

where t is the time in days. The initial population (when t=0) is 1000. Write an equation that gives the population at any time t, and find the population when t=3 days.
$\frac{dP}{dt} = \frac{3000}{1+0.5t}$

$dP = 3000 \times \frac{dt}{1+0.5t}$

$\int {dP} = 3000 \int \frac{dt}{1+0.5t}$

$P = 3000 \int \ln{|1+0.5t|} + C$

If you plug in t = 0, P = 1000, you can find C.