Question

At 10:05 a.m., there are 2 microscopic bacteria cells in a bottle .at 10:15a.m., there are 8 cells one the bottle. What time will there be 16 cells in a bottle

Answer 1

This is exponential growth...

f=ir^t, f=final amount, i=initial amount, r=rate, t=time 

f=2r^t so we have a point at ten minutes that says:

8=2r^10

4=r^10

r=4^(1/10) so our equation is:

f=2(4^(1/10)^t)

f=2(4^(t/10))  now we wish to solve for t when f=16

16=2(4^(t/10))

8=4^(t/10)  taking the natural log of both sides...

ln8=(t/10)ln4

t/10=ln8/ln4

t=10(ln8/ln4)

t=15

So after fifteen minutes there will be 16 cells in the bottle...

10:05+:15=10:20

So at 10:20 there will be 16 cells in the bottle.