1. From week#2 discussion on exponential functions

2. Populations tend to growth exponentially not linearly When an object cools (e.g., a pot of soup on the dinner table), the temperature decreases exponentially toward the ambient temperature (the surrounding temperature) Radioactive substances decay exponentially Bacteria populations grow exponentially Money in a savings account with at a fixed rate of interest increases exponentially Viruses and even rumors tend to spread exponentially through a population (at first) Anything that doubles, triples, halves over a certain amount of time Anything that increases or decreases by a percent 2

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4. Remember that exponential equations are in the form: y = P(1+r) x  P is the initial (reference, old) value  r is the rate, a.k.a. percent change (and it can be either positive or negative)  x is time (years, minutes, hours, seconds decades etc…)  Y is the new value 4

5. Applying exponential formula to saving account applications…

6.  Putting your money into a savings account is like loaning the bank your money  Buying savings bonds you actually loan money to the government  In return the bank/government pays you interest…  And gets to use your savings to generate more money  Through investments, loans, etc…

7.  The amount of interest you are paid for loaning your money  Formula for using APR is  A=P*(1+r/n)^(nY)  P = beginning balance  r = annual interest rate (APR)  n = compounding frequency (1=annually, 4 = quarterly, 12 = monthly)  Y = number of years

8.  You deposit $800 into a savings account that has an annual percentage rate of 2.1% compounded quarterly.  What is your balance after the first year?  A=P*(1+r/n)^nY)  A=800*(1+.021/4)^(4*1)  A=$816.93  What is your balance after 5 years?  How long would it take your money to double?  Hint: Use logs

9.  Use the percentage increase/decrease formula  In this case Y=P*(1+r)^x  The equation?  1600 = 800*(1+.021/4)^4x  Divide by 800  2 = (1.00525)^4x  Take log of both side  Log 2 = log(1.00525)^4x  Follow rule #2  Log 2= 4x* log(1.00525)  Divide by log(1.00525)  33.35 years to double your money

10.  Percentage rate reflecting the total interest to be earned based on:  the interest rate  an institution’s compounding method  assuming funds remain in account for a 365-day year.  Formula  Use Percentage change formula for 2 consecutive years  =(new-old)/old  Change value to a %, show 2 decimal places

11.  Check out this link  ABC's of Figuring Interest ABC's of Figuring Interest