Section 5.2b The Natural Exponential Function
Objective 4: Solving Applications of the Natural Exponential Function
Continuous Compound Interest Formula
Continuous compound interest can be calculated using the
formula
rt
A Pe
where
A
Total amount after t years
P
Principal
r
Interest rate per year
t
Number of years
5.2.21
How much money will there be in an account at the end of 8 years if $14,000 is deposited at a 7.5% annual rate
that is compounded continuously?
Exponential Growth
A model that describes the population, P, after a certain time, t, is
0
( ) kt
P t P e
where
0(0)P P
is the initial population and
0k
is a constant
called the relative growth rate. (Note:
k
may be given as a percent.)
In 1975, a wildlife resource management team introduced a certain rabbit species into a forest for the first time.
In 2007 the rabbit population had grown to 6454. The relative growth rate for this rabbit species is 22%.
a) How many rabbits did the wildlife resource management team introduce into the forest in 1975?
b) How many rabbits can be expected in the year 2021?
0
( ) kt
P t P e
0
0, P