Question

A bacteria culture starts with 1,500 bacteria and doubles in size every 4 hours. Find an exponential model for the size of the culture as a function of time t in hours

Answer 1

a(t)=Ae^rt

Answer 2

3000=1500e^4r

Answer 3

ln2=4r

Answer 4

t=ln2/4

Answer 5

a(t)=Ae^(ln2)t/4

Answer 6

sry... r = (ln2)/4 the last answer is still correct

Answer 7

Valpey, what do you think?

Answer 8

P = Noe^(kt)
where
P is amount after t time
No is the initial amount
.
No is 1500

bacteria doubles in size every 4 hours

so when t=4, P = 3000

3000 = 1500e^(4k)
2= e^(4k)
ln(2) = 4k
ln(2)/4 = k
0.17328679513999 =k

so k=0.1733

P = 1500e^(0.1733t)



so required equation is
.
F(t) = 1000e(0.34657t)

Answer 9

initially its 1500
after 4hrs it becomes 1500*2
after 8 hrs----> 1500*2^2
after 12hrs---->1500*2^3
.
.
.
after 4*t hrs---->1500*2^t

so after t hrs its given by
\[1500*2^t/4\]