1. 10.7 Exponential Growth and Decay

2. (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)

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

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

5. 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

6. 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

7. 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

8. 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

9. 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 ?

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