1. Exponentials and Logarithms
Applications:
Exponentials and Logarithms
Objective:
Be able to solve problems involving compounding interest.
Be able to determine the exponential growth and decay of various populations
Critical Vocabulary:
Principal, Rate, Compounding, Growth, Decay, Exponential Law, Uninhibited Growth or Decay

2. Simple Interest Formula
P = Principal (The amount that you start with)
R = Interest Rate (Written in Decimal Form)
N = Number of times compounded per year
T = Amount of time (in years)

3. John has $2500 that he wants to invest over a period of one year
John has $2500 that he wants to invest over a period of one year. Fill in the following chart based on the interest rate of 6.2%.
Compounded
# of Times
Formula
Value of “A”
Annually 1 $
Semi-Annually 2 $
Quarterly 4 $
Monthly 12 $
Daily
365 $
Hourly
8,760 $
Minutely $
525,600
Continuously $

4. Example 1: Find the principal needed to get $2500 after 3 years at 5%
compounded monthly?
You made $347.56

5. It will take about 24 years to triple an investment.
Example: How long would it take far an investment to triple at a
rate of 4.6% compounded quarterly?
It will take about 24 years to triple an investment.

6. Exponential Law
Law of Uninhibited Growth/Decay
A = Aoekt
N(t) = Noekt
A0 = Initial Population
N0 = Initial Population
k = constant
k = constant
T = Amount of time
T = Amount of time
A = New population
N(t) = New population

7. Example:
The growth of an insect population obeys the equation A = 700e0.07t where t represents the number of days. After how many days will the population reach 3000 insects?

8. Example:
A culture of bacteria obeys the law of uninhibited growth. If there are 800 bacteria present initially, and there are 1100 present after 2 hours, how many will be present after 7 hours?
1st: Find the “k” value
2nd: Find the amount after 7 hours

9. Example:
The half-life of an element is 1710 years. If 15 grams are present now, how much will be present in 40 years?
1st: Find the “k” value
2nd: Find the amount after 40 years

10. “Compounding Interest”
Joe wants to invest $3, in a CD (Certificate of Deposit) for 1 year. His bank is offering to compound the interest monthly at a rate of 4.23%. How much will he have when the CD matures?
Andy invests $2, in a CD at an interest rate of 4.6% for 9 months. If the interest gets compounded continuously, how much will he have at the end of the term?
How many years will it take for an initial investment of $7, to grow to $9, at a rate of 6% compounded quarterly?
How many years will it take for an investment to triple if it is invested at 7.4% per annum compounded monthly? What if it were compounded continuously?
In three years you want to purchase a TV that costs $ The bank is currently offering an interest rate of 5.25% compounded daily. How much should your initial investment be so you can buy the TV in three years?
How long will it take for $1,300 to turn into $5,000 at and interest rate of 6.7% per annum compounded semiannually? What if it were compounded continuously?