# exponential decay ```02.06.12_02.07.12: Exponential Growth and Decay
*students will model real world situations to develop the exponential growth (and decay) function.
1. Students will work on the “try it out” scientific notation problem and 5 exponent practice problems.
 Demonstrate on the calculator
2. Grade “Practice with Scientific Notation”.
3. Exponential Growth and Decay
 If I deposited \$1,000 in my savings account at the bank and I earned 8% interest, compounded yearly, how much
would my savings increase over time?
o Terms: annual interest, compound interest (interest calculated on both the principal (initial amount) and the
accrued interest.
 Make a table.
Years
(X)
Account Balance (Y)
0
1
2
3
x
Amount of
Interest
Earned that
Year
\$1,000
1(\$1000) + (0.08)(\$1,000) = 1.08 (\$1,000)
1 (1.08)(\$1,000) + (0.08) [(1.08)(\$1,000)] = 1.08 [1.08 (\$1,000)] = (1.08)2(\$1,000)
1[(1.08)2(\$1,000)] + 0.08 [(1.08)2(\$1,000)] = 1.08 [(1.08)2(\$1,000)] = (1.08)3(\$1,000)
\$0
\$80
\$86.40
\$93.31
(1.08)x(\$1,000)
 Equation: 𝑦 = (1,000)(1.08)𝑥
 Account balance = (principal/initial amount) [1 + rate (as a decimal)]time
 Show what the graph looks like on the calculator.
 EXPONENTIAL GROWTH: y = a (1 + r)
t







o
o
o
200 = 100 (1.06)t
200/100 = (1.06)t
o Let a = initial amount / principal
 EXPONENTIAL DECAY: y = a (1 + r) t
o Let t = time
o Same formula, but the rate is negative
o Let r = growth rate
 I bought a computer for \$2,000, but it loses
After 20 years, how much money would I have
value at a rate of 56% annually. How much is it
accrued in the bank?
worth after 1 year, 2 years, 3 years, and 4 years?
o y = (1000)(1+0.08)20 = \$4,660.96
Years
Worth (y)
 I earned \$3660.09 just by
(x)
letting money sit in the bank!
0
2000 (1-0.56)0 = 2000 (0.44) 0= 2000
If you deposited \$100 worth of birthday money
(1) = 2000
in your savings account and earned 6% interest
1
2000 (0.44) 1= \$880
compounded annually, how much would you
2
2000 (0.44) 2= \$387.20
have in the bank after 1 year, 2 years, 5 years,
3
2000 (0.44) 3= \$170.37
and 10 years?
4
2000 (0.44) 4 = \$74.96
o y = 100 (1 + 0.06)x = 100 (1.06)x
o Show what the graph would look like.
Year (x)
Balance (y)
1

I
bought
a car that costs \$26,000. It loses value
1
100(1.06) = \$106
2
at a rate of 20% annually. How much will it be
2
100(1.06) = \$112.36
5
worth after 5 years?
5
100(1.06) = \$133.82
10
o y = 26,000 (1 + -0.2) 5
10
100(1.06) = \$179.08
o
= 26,000 (0.8) 5
How long would it take for your money to
o
= 8,519.68
double?
t
o y = 100 (1.06)
Other examples: cost of health care, growth of a colony of bacteria, population increase, increase in college tuition,
etc.
HW 3.12: Exponential Growth and Decay
On Thursday students will take a practice EOC in study labs.
3.2 Quiz on Friday, 2/10, and Mon, 2/13
```