Exponential Growth - HP 39gs Master Manual

E x p o n e n t i a l g r o
E x p o n e n t i a l g r o
A population of bacteria is known to follow a growth pattern governed by the equation
= ; t ≥ 0
kt
N N
0
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 using the calculator.
N
0
Step 1. Start up the Statistics aplet, set it to
given. Change to the
Exponential line of best fit for the data.
Step 2. Press
VIEWS
not appear then press
line draws.
Step 3. Change to the
of the regression line and press
places, this gives an equation of:
N =
13 8950e
w t h
w t h
. It is observed that at t = 3 hours, there are 100 colonies of bacteria and that at
and of k.
N
0
SYMB SETUP
and choose Auto Scale. If the line shown does
and then
view, move the highlight to the equation
SYMB
⋅ ⋅
0 6579 t
and enter the data
view and specify an
. Wait while the
. Rounded to 4 dec.
305