# Determining time and remaining amounts.  PERT!  A = Pe rt (sure is purdy, isn’t it?!)  A = After amount  P = Principle (Starting amount)  R = Interest.

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Determining time and remaining amounts

 PERT!  A = Pe rt (sure is purdy, isn’t it?!)  A = After amount  P = Principle (Starting amount)  R = Interest Rate (divided by 100)  T = time (in years)

Maggie is saving up money to buy her first car. She has \$3,500 to put in the bank for 5 years. How much money will she have if she gets an interest rate of 7.9%?

A = ? P = 3500 R = 7.9% = 0.079 T = 5 A = 3500e 0.079*5 = \$5,195.34

We need to use log! No, not that kind of log!

You decide that you want to deposit some money in the bank. You want to put \$25 in and save it. The bank meant to give you a rate of 8%, but they made a typo and ended up giving you a rate of 80%. How long will it take you to get to \$100

Steps 1. Divide both sides to get the base and exponent alone 2. Ln both sides 3. Bring the exponent to the front 4. Isolate t to solve Example 100 = 25e 0.8t 4 = e 0.8t Ln 4 = Lne 0.8t Ln 4 = 0.8tLne Ln 4 = 0.8t Ln 4 ÷ 0.8 = t 1.73 = t *It will take 1.73 years to reach \$100

Practice!!! Pg. 163 #2: t = 20.996 #3: t = 69.31 Pg. 167 #3: t = 16.22 #4: t = 15.40

 Definition: the amount of time necessary for half of a substance to disappear  Formula:  N 0 = After Amount  N 1 = Starting Amount  T = time  T.5 = length of 1 half-life When not given a starting amount, use 100!

The D.J. at the prom starts the evening with a playlist of 15,000 songs. Right before the prom, his computer gets a virus causing half of the playlist to not work after 40 minutes. How many songs will he have left if the prom lasts 120 minutes?

Steps 1. Determine your variables and fill in 2. Simplify 3. Solve Example N 0 = ? N 1 = 15000 T = 120 T.5 = 40

1) 12.5 mg 2) 62.996 mg 3) 8.8978% 4) 86.446%

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