10.7 Exponential Growth and Decay

(move decimal pt 2 places left) Compound Interest A = P (1 + r/n)nt A = compound amt P = principal amt r = rate n = # of compounds per year t = time (years) (amt end with) (amt start with) inc + dec – (%  decimal) (move decimal pt 2 places left)

Growth Formula N = N0∙2t/d N = new population N0 = orig pop t = time d = doubling time units must match

Decay Formula N = N0(1/2)t/h N = new population N0 = orig pop t = time h = half life units must match

Example 1 A = P (1 + r/n)nt A = ? P = $1,000 r = 12% n = 2 t = 5  .12 One thousand dollars is invested at 12% interest compounded semi-annually. Determine how much the investment is worth after 5 years. A = P (1 + r/n)nt A = ? P = $1,000 r = 12% n = 2 t = 5  .12

Example 3 N = N0∙2t/d N = ? N0 = d = 20 min N0 t = 1 hour  60 min A culture of yeast doubles in size every 20 minutes. Find its size in 1 hour. N = N0∙2t/d N = ? N0 = d = 20 min t = 1 hour They don’t tell us N0 N0  60 min Your answer is left in terms of N0

Example 4 N = N0(1/2)t/h N = ? N0 = h = 3.8 days t = 1 week 100 mg The half-life of radioactive gas radon is 3.8 days. How much of 100 mg of the gas will be left after 1 week? N = N0(1/2)t/h N = ? N0 = h = 3.8 days t = 1 week 100 mg  7 days

Example 2 A = P (1 – r/n)nt A = ? P = 12,500 r = 20% n = 1 t = 10 The value of a new $12,500 automobile decreases 20% per year. Find its value after 10 years. A = P (1 – r/n)nt A = ? P = 12,500 r = 20% n = 1 t = 10  .20

Example 5 A = P (1 + r/n)nt A = P = r = n = t = 3P P 6%  .06 1 ? How long will it take you to triple your money if you invest it at a rate of 6% compounded annually? A = P (1 + r/n)nt A = P = r = n = t = 3P P 6%  .06 1 ?

Homework #5 Pg. 486 (Problems) 3c, 6c, 7b, 9a 10, 11