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 1992 93 94 95 96 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 ofExponential

Growth

Simple InterestA = P(1 + r)t

Compound InterestA = P(1 + r/n)nt

ContinuousCompounding

A = ert

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?