Exponential and
Logarithmic Functions
 The
 The
number e
number e is like

It is transcendental. It cannot occur as the
root of any polynomial function with
rational coefficients.
e is approximately 2.718
 Exponential
Growth or Decay
 in terms of e
 Example # 1
 According to Newton, a beaker of liquid cools exponentially
when removed from a source of heat. Assume that the
initial temperature T is 90 degrees F and that k = .275.
Write a function to model the rate at which the liquid cools.
2. Find the temperature T of the liquid after 4 minutes (t)
3. Graph the function and use the graph to verify your answer
in #2
3.
Solution:
kt
1. T = T1e
.275 ( 4 )
2. T = (9 0 )e
≈ 3 0 d eg rees F
1.
 Continuously
Compounded Interest
Some banks offer accounts that compound the interest
continuously. The formula for finding continuously
compounded interest is different from the one used for
interest that is compounded a specific number of times each
year.
 Example

#2
Compare the balance after 30 years of a $15,000
investment earning 12% interest compounded continuously
to the same investment compounded quarterly.
. 1 2( 3 0 )

Continuously: A = 15000 e

4( 30)
Quarterly: A = 15000 ( 1+ .12/4)
= $520,664.81

= $548,973.52
% of change: (548973.52-520664.81)/520664.81
=28308.71/520664.81=.05437 or 5.44% more
 HW
# 27
Section 11-3
Pp. 714-717
#6,8,10,11,18,23