1) Write the following in Scientific Notation 17,000,000,000,000 = 1.7 × 10 13 2) Write the following without Scientific Notation 9.3 × 10 – 3 = 0.0093 3) Simplify ( 4 × 10 8 )( 2 × 10 – 2 ) = 8 × 10 6 4) Simplify 3 × 10 2 ________ = 6 × 10 – 7 = 0.6 × 10 – 6 5 × 10 8

12.06 Exponential Growth

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.

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 ( 1 + .10 ) 20 = 1345.49 1345 Wolves

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 = 50000 ( 1 + .05 ) 4 = 60775.3125 $ 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 = 10000 ( 1 + .08 ) 3 = 12597.12 $ 12,597.12

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 = 2000 ( 1 + .12 ) 35 = 105599.2392 $ 105,599.24

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 ( 1 + .07 ) 14 = 128.92677075 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 = 10000 ( 1 + .025 ) 10 = 12800.84544 $ 12,800.85