1. Objective: To use exponential and logarithmic functions to solve problems.

2. Compound Interest Continuous Compounding Exponential Growth or decay (bacteria/ radiation half life) Richter Scale

3. Compound interest means the each payment is calculated by including the interest previously earned on the investment.

4. Year Investment at StartInterestInvestment at End 0 (Now)$1,000.00 ($1,000.00 × 10% = ) $100.00 $1,100.00 1 ($1,100.00 × 10% = ) $110.00 $1,210.00 2 ($1,210.00 × 10% = ) $121.00 $1,331.00 3 ($1,331.00 × 10% = ) $133.10 $1,464.10 4 ($1,464.10 × 10% = ) $146.41 $1,610.51 5

5. If you have a bank account whose principal = $1000, and your bank compounds the interest twice a year at an interest rate of 5%, how much money do you have in your account at the year's end?principal interestan interest rate

7. When n gets very large it approaches becoming continuous compounding. The formula is: P = principal amount (initial investment) r = annual interest rate (as a decimal) t = number of years A = amount after time t

8. An amount of $2,340.00 is deposited in a bank paying an annual interest rate of 3.1%, compounded continuously. Find the balance after 3 years. Solution A = 2340 e (.031)(3) A = 2568.06

9. A = Pe rt...or... A = Pe kt...or... Q =e kt...or... Q = Q 0 e kt k is the growth constant

10. In t hours the number of bacteria in a culture will grow to be approximately Q = Q 0 e 2t where Q 0 is the original number of bacteria. At 1 PM the culture has 50 bacteria. How many bacteria does it have at 4 PM? at noon? Q = 50e 2(3) Q = 50e 2(-1) Q = 50e 6 Q = 50e -2 Q = 20,248 Q = 7

11. 1. If you start a bank account with $10,000 and your bank compounds the interest quarterly at an interest rate of 8%, how much money do you have at the year’s end ? (assume that you do not add or withdraw any money from the account)interest rate 2. An amount of $1,240.00 is deposited in a bank paying an annual interest rate of 2.85 %, compounded continuously. Find the balance after 2½ years.

12. 1. 2. A = 1240e (.0285)(2.5) = $1,331.57

13. The first credit card that you got charges 12.49 % interest to its customers and compounds that interest monthly. Within one day of getting your first credit card, you max out the credit limit by spending $1,200.00. If you do not buy anything else on the card and you do not make any payments, how much money would you owe the company after 6 months? A = P(1 + ) nt

14. An artifact originally had 12 grams of carbon-14 present. The decay model A = 12e -0.000121t describes the amount of carbon-14 present after t years. How many grams of carbon-14 will be present in this artifact after 10,000 years? A = 12e -0.000121t A = 12e -0.000121(10,000) A = 12e -1.21 A = 3.58

15. R = log It compares how much stronger the earthquake is compared to a given standard R= 3.0 then 3 = log 1000 = I = 1000I 0 1000 times the standard

16. Haiti 7.0 7 = log 10,000,000 = Japan 8.9 8.9 = log 794,328,235 = Virginia 5.9? (August 23, 2011) 794,328