A certain type of bacteria increases continuously at a rate proportional to the number present. if there are 500 bacteria at a given time and 1000 present 2 hours later, how many will there be 5 hours from the initial time given?

dP/dt = kP

dP=kPdt

∫dP/P = k ∫dt

ln|P| = kt + C

P = Ce^kt

P= P0e^kt

1000 = 500e^2k

2 = e^2k

ln2= 2k

k=ln(2) /2

P = 500e^5(ln2/2)

P=2828.4