Aculture started with 5,000 bacteria. after 2 hours, it grew to 6,500 bacteria. predict how many bacteria will be present after 18 hours. round your answer to the nearest whole number.

This can be expressed as exponential growth of the form:

f=ir^t, f=final amount, i=initial amount, r=common ratio (rate), t=time

In this case we are given the point (2, 6500) and i=5000 so we can solve for the rate...

6500=5000r^2  divide both sides by 5000

1.3=r^2  take the square root of both sides and note that we know r>0

r=1.3^(1/2) so our equation becomes:

f=5000(1.3)^(1/2)^t  and knowing that (a^b)^c=a^(b*c) we can say:

f=5000(1.3)^(t/2)  so for t=18

f=5000(1.3)^9

f≈53022  (to nearest whole bacteria)

None liner bro because