A bacterial culture starts with 2000 bacteria and doubles every .75 hours. Write an exponential function that models the sample's growth over time.after how many hours will the bacteria count be 32000?
+128578 Using
N = 2000ekt where N is the number of bacteria at any time, t ≥ 0........
We need to solve for the constant k........and we're told that......
4000 =2000ek(.75) divide both sides by 2000
2 = e.75k take the natural log of both sides
ln2 =lne.75k and by a log property, we can write
ln2 =.75k (lne) and lne = 1 ......so....
ln2 =.75k divide both sides by .75
k = ln2/.75
So, our function is
N =2000e(ln2/.75)t
And to find out when N = 32000, we have
32000= 2000e(ln2/.75)t divide both sides by 2000
16 = e(ln2/.75)t take the ln of both sides
ln 16 = lne(ln2/.75)t and we can write
ln 16 = (ln 2/.75)t divide both sides by ln2/.75
[ln16]/ [ln2/.75] = t = 3 hrs.
+128578 Using
N = 2000ekt where N is the number of bacteria at any time, t ≥ 0........
We need to solve for the constant k........and we're told that......
4000 =2000ek(.75) divide both sides by 2000
2 = e.75k take the natural log of both sides
ln2 =lne.75k and by a log property, we can write
ln2 =.75k (lne) and lne = 1 ......so....
ln2 =.75k divide both sides by .75
k = ln2/.75
So, our function is
N =2000e(ln2/.75)t
And to find out when N = 32000, we have
32000= 2000e(ln2/.75)t divide both sides by 2000
16 = e(ln2/.75)t take the ln of both sides
ln 16 = lne(ln2/.75)t and we can write
ln 16 = (ln 2/.75)t divide both sides by ln2/.75
[ln16]/ [ln2/.75] = t = 3 hrs.
