Table of Contents
Advertisement
E
x
p
o
n
e
n
t
i
a
l
g
r
E
x
p
o
n
e
n
t
i
a
l
g
r
A population of bacteria is known to follow a growth pattern governed
by the equation
there are 100 colonies of bacteria and that at t = 10 hours there are
10,000 colonies.
(i)
Find the values of
(ii)
Predict the number of bacteria colonies after 15 hours.
(iii)
How long does it take for the number of colonies to double?
(i) Find
and k.
N
0
Step 1. Start up the Statistics aplet, set it to
and enter the data given.
Change to the SYMB SETUP view and
specify an Exponential line of best fit
for the data.
Step 2. Change to the PLOT SETUP view and
adjust it so that it will display the data.
(This is not really needed, since the
line of best fit is what we need and it
will be calculated even if the data
doesn't show.) YTick is set to 1000
incidentally.
Now change to the PLOT view and
press
while the line draws.
Step 3. Change to the SYMB view, move the
highlight to the equation of the
regression line and press
Rounded to 4 dec. places, this gives
an equation of:
=
N
13 8950
o
w
t
h
o
w
t
h
=
≥
kt
N
N e
;
t
0
N
(if not already set). Wait
⋅
⋅
0 6579
t
e
. It is observed that at t = 3 hours,
0
and of k.
0
.
291
Hide quick links:
Advertisement
Table of Contents
