Natural Logarithms
Section 8.6
Recall that e  2.718...
Natural Logs
ln
loge
ln 1 = loge 1  ?
Evaluate
1. ln e
3
2. ln e
2
3. ln e
5
log e
4.
2
5. ln  5 
Using Natural Logs to solve equations.
1. 7e  2  23
2x
x
3
2. e  5  10
How long would it take an investment to double
if it is compounded continuously at 3.25%?
A  Pe
rt
Solving Natural Log Equations
1. ln 3x  27
x 1
2. ln
5
3
Solving Natural Log Equations
3. ln x  2 ln 3  4
1
3
4. ln  5x  3  2
Write an exponential equation then solve
1. Carbon-14 is used to study fossil remains. It has a
half-life of 5760 years. What is the age of a fossil
with 1/5 of its carbon-14 remaining?
2. Medical research indicates that the risk of having a
car accident increases exponentially as the
concentration of alcohol in the blood increases. The
risk is modeled by: R=
, where x is the blood
alcohol concentration and R, given as a percent, is
the risk of having a car accident. What blood alcohol
concentration corresponds to a 17% risk of a car
accident?
3. The exponential decay model for Carbon-14 is
y  ne
.000121t
Prehistoric cave paintings were discovered in a
cave in France. The paint contained 15% of the
original carbon14. Estimate the age of the
paintings.
Homework
Workbook 8-6 #7-45 odd
Wkst: word problems
Page 465 #14-38