(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
Applications of Exponential Growth
A colony of bacteria may grow at a rate proportional to its size.
Other populations, such as those of humans, rodents, or fruit flies, whose
supply of food is unlimited may also grow at a rate proportional to the size of
the population.
Money invested at interest that is compounded continuously accumulates at a
rate proportional to the amount present. The constant of proportionality is the
interest rate.
The demand for certain precious commodities (gas, oil, electricity, valuable
metals) has been growing in recent decades at a rate proportional to the
existing demand.
Each of the above quantities (population, amount, demand) is a function of
the form cekt (with k > 0). (See Figure N9–7a.)
Radioactive isotopes, such as uranium-235, strontium-90, iodine-131, and
carbon-14, decay at a rate proportional to the amount still present.
If P is the present value of a fixed sum of money A due t years from now,
where the interest is compounded continuously, then P decreases at a rate
proportional to the value of the investment.
It is common for the concentration of a drug in the bloodstream to drop at a
rate proportional to the existing concentration.
As a beam of light passes through murky water or air, its intensity at any
depth (or distance) decreases at a rate proportional to the intensity at that
depth.
Each of the above four quantities (5 through 8) is a function of the form ce
−kt (k > 0). (See Figure N9–7b.)