PreCalc 12/11
Unit 1 Logs
Day 3 Notes
e problems
Just like  is a special symbol that represents a number, so is e. There are two important
logs in life, we’ve seen the typical one with base 10 often used. The other is the log that
base base e in which is written as ln(x). We use the letter e whenever we have a growth
or decay problem that is continuous. Our Porn formula also gets a slight change but is
used kind of the same.
P = Poekt
Ex 1
A bacteria grows continuously at a rate of 8% a day. If we started with 3g of bacteria,
how much do we have after 25 days?
Ex 2
Thomas invests money and gets 7.5% continuous interest. How long will it take him to
double his money?
Matty 2014
Math 12
Unit 2 Logs & Sequences Day 3 Notes Page 2
HW:
1.
A certain strain of bacteria grows continuously from 40 to 326 in 120 minutes.
Fink k for the growth formula during the 120 minutes. (answer = 0.0175)
2.
A current census shows that the population of a city is 3.5 million. Using the e
formula, find the expected population of the city in 30 years if the continuous growth rate
of the population is 1.5% per year. (answer = 5.49 million)
Matty 2014