There are many situations
where the increase or decrease of some variable in a fixed time interval
will be proportional to the magnitude of the variable at the beginning
of that time interval.
There are many situations
where the increase or decrease of some variable in a fixed time interval
will be proportional to the magnitude of the variable at the beginning
of that time interval.
For example, let's look at a population of wee beasties which increases by 10% per year. If there were 100 wee beasties now, there would be an increase of 10 wee beasties after a year. We would see an increase of 500 wee beasties in a year when there were 5000 at the beginning.
Likewise, we can look at a population which decreases by 50% (i.e. a decrease to 1/2, or by a factor of 2) every day. A population of 100 would be down to 50 a day later, and a population of 5000 would drop to 2500 after one day.
These are all examples of exponential growth and decay.
A single equation can be
used to solve all problems involving this type of change:
'
is the initial number, 'k' is the growth constant (if positive)
or the decay constant (if negative), and 'e' is the base
of natural logarithms (approximately 2.71828).
We can re-write this equation in another convenient form. Dividing the
equation by , and then taking the
natural logarithms of both sides, we get
'; all we need to know here is the
ratio of these two values.
These two problems are used to solve questions for both exponential growth and exponential decay.
Continue to:
Exponential Growth
Continue to:
Exponential Decay
Return to:
Exponential Growth and Decay Menu
Exit to:
Physics Tutorial Menu