1. 1) Write the following in Scientific Notation
17,000,000,000,000
= ×
2) Write the following without Scientific Notation
9.3 × 10 – 3 =
3) Simplify
( 4 × 10 8 )( 2 × 10 – 2 )
= 8 × 10 6
4) Simplify
3 × 10 2
________
= 6 × 10 – 7
= × 10 – 6
5 × 10 8

2. Exponential Growth

3. If the amount of something increases exponentially over a period of time, it is called exponential growth.
Compound interest is a typical example of exponential growth.
To compute exponential growth, use the formula:
y = the ending amount,
C = the initial amount,
r = the rate (expressed as a decimal),
t = the amount of time.

4. Exponential Growth
To find the amount (y) that results from an initial amount (C) given a certain rate (r), over a given period of time (t), replace the variables with their given amounts and simplify.
The wolf population in Chicago is growing at a rate of 10% per year. If there are 200 wolves today, how many will there be in 20 years?
y = 200 ( ) 20 =
1345 Wolves

5. Exponential Growth y = 50000 ( 1 + .05 ) 4 = 60775.3125 $ 60,775.31
A company had sales of $50,000 last year. They are projecting a yearly growth of 5% each year. What is the projected yearly sales after 4 years?
y = ( ) 4 =
$ 60,775.31
College tuition has been increasing by 8% each year. If the trend continues, what will a yearly $10,000 tuition cost in 3 years?
y = ( ) 3 =
$ 12,597.12

6. P = principle (amount invested ) r = rate ( interest rate ) t = time
Another type of exponential growth is compound interest.
A = account balance
P = principle (amount invested )
r = rate ( interest rate )
t = time
A man puts $2000 into an IRA account earning 12% per year. If no more money is added, how much will he have after 35 years?
A = ( ) 35 =
$ 105,599.24

7. Try This: y = 50 ( 1 + .07 ) 14 = 128.92677075 128 Fruit Flies
A student begins with 50 fruit flies. If the fruit flies increase by 7% each day, how many fruit flies will there be after 2 weeks ( 14 days )?
y = 50 ( ) 14 =
128 Fruit Flies
A man invests $10000 into a CD earning 2.5% each year over a 10 year period. How much money will he have after 10 years?
C = ( ) 10 =
$ 12,800.85