A bacteria population grows such that growth rate is proportional to population. At t=0 there are 100000 bacteria. At 48 hours there are 300000. How many bacteria will there be at t=72 hours?

Question

1601 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-02T16:50:36

Population after $72$ hrs is $519615$ after rounding up.

General form of equation for natural growth [exponential] is

$P=Ce^[kt]$ . So given that at time $=0$ , population is 100,000 we have....

$100,000 =Ce^[k[0]$ and since $e^[k[0]$ =1, then $C=100,000$ and so

$P=100,000e^[kt$ . And thus , when the population is $300,000$ at time $t=48$

$300,000=100,000e^[48k$ , solving this for $k$

ln $3= 48k,$ ie $k=ln3/48$ , which is $0.022889$ to six decimal places.

This now gives $P=100,000e^[.022889t]$ ........... $[1]$ , and
substituting $t=72$ into $[1]$

$P=100,000e^[1.647918]$ which gives $P=519615$