Step-by-step explanation:
A biologist is researching a newly-discovered species of bacteria.
at time t=0 hours, he puts one hundred bacteria into what he has determined to
be a favorable growth medium.
Six hours later, he measures 450 bacteria.
Find an exponential equation that approximates the information.
:
find k, the growth factor
100*(2^(6/k)) = 450
Divide both sides by 100
2^(6/k) = 4.5
use logs here
log(2^(6/k)) = log(4.5)
:
log(2) = log(4.5)
=
= 2.17
k =
k = 2.765 is the growth factor
:
A = Ao*2^(t/2.765), the exponential equation
where
Ao = initial amt
A = amt after t hrs
