Hope this helps to guide you
The count in a bacteria culture was 700 after 20 minutes and 1000 after 40 minutes. What was the initial size of the culture?
490 microorganisms.
Explanation:
I will assume exponential growth for bacteria. This means that we can model the growth with an exponential function:
f
(
t
)
=
A
0
e
k
t
where
k
is the growth constant and
A
0
is the initial amount of bacteria.
Sub the two known values into the function to get two equations:
700
=
A
0
e
20
k
(1)
1000
=
A
0
e
40
k
(2)
Divide (2) by (1) to find
k
:
1000
700
=
A
0
e
40
k
A
0
e
20
k
10
7
=
e
40
k
−
20
k
=
e
20
k
Take the natural log of both sides to isolate
k
:
ln
(
10
7
)
=
ln
e
20
k
ln
(
10
7
)
=
20
k
k
=
ln
(
10
7
)
20
Now that we have the growth constant,
k
, we can substitute one of the points in to solve for the initial amount,
A
0
:
(
40
,
1000
)
1000
=
A
0
e
ln
(
10
7
)
20
⋅
40
A
0
=
1000
e
0.0178
⋅
40
=
490
Answer:
Estimate the following (by rounding off to nearest hundred (a)6,941 (b)6,320 (c) 416 (d)126 (e)109 (f)202 (g) 146 (h)7,699 (I)8,311 (j)986
Step-by-step explanation:
