Exponential growth - Word Format

# Exponential growth - Word Format - Exponential growth/decay...

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Exponential growth/decay The basic idea is that “something” grows or decays at a certain percentage rate. That rate is given “per unit of time”. One key to remember is that “1” is the multiplicative identity, i.e. multiplying by 1 DOES NOTHING. So if something grows at 5% then we need to multiply 5% by MORE THAN 1, or in other words the factor would be 1.05. For this overview, let’s first concentrate on “bank accounts”. Let’s assume that you have a bank where you deposit \$1000 at 5% simple interest/year. So to find the balance AFTER one year (i.e. at the beginning of the second year) you’d multiply \$1000 by 1.05- Remember that if I multiply by 1, NOTHING happens…Balance = 1000 * 1 = 1000 if you multiply by 1 you get ONLY your original balance of \$1000 back with NO interest. So you multiply by 1 AND by 5% to get your deposit back AND interest- 1000*(1+0.05) = 1000*1 + 1000*0.05 = 1000 + 50 =1050 We use the shorter version- Balance = 1000*1.05 = 1050 SO after one year we have 1000*1.05 dollars. So to find out the balance B after the NEXT (second year) we’ll multiply again by 1.05 – B=(1000*1.05)*1.05 or From here I hope you see that we take the “initial value” and multiply by the “growth factor” F (in this example 1.05) to the power of t (how many times the growth factor occurs) P = Example 1 A bank account has an original balance of \$2000. It grows at 5% per year.

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