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Determining time and remaining amounts

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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)

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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%?

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

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

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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

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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

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

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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!

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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?

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

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

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