More Exponential Growth… Growth and Decay—Real Life!!!

Growth In 1992, a pound of bacon sold for $2. Prices have risen the last 20 at a rate of 2% per year. If it increased the same amount every year, how much should bacon be sold for now (2012)?

Bacon increases by 2% annually Year n years Cost$3.00 Increase rate n/a

Can you come up with an equation to model this situation? Cost = initial price (rate) time. P = 3(1.02) t If this trend continues, how much will a pound of bacon cost in 2042?

What if something decreases in value? Cars depreciate at an average of 15% a year once you drive them off the lot. If you bought a car for $30,000, how much would it be worth in –3 years? –10 years? –40 years?

Finding the rate… Your family invested $500 in a bank account for you at age 13. At age 30, having never touched the money, you now have $1200 in the account. What was the interest rate your account gained annually?

Types of Exponential Growth Simple Interest A = P(1 + r) t Compound Interest A = P(1 + r/n) nt Continuous Compounding A = e rt

You invest $1500 in an account that gains 2.5% per year. If you don’t touch the money for 20 years, how much will it be worth if it is compounded: –Annually? –Quarterly? –Monthly? –Weekly? –Daily? –Continuously?