Question 73053
Given:
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{{{A = A[o]*e^(-0.18t)}}}
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When t = 3 days, then you are told that A (the amount remaining) is 40 grams. Substitute
these values into the equation to get:
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{{{40 = A[o]*e^(-0.18*3)}}}
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You need to solve this for {{{A[o]}}}
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First multiply out the exponent:
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{{{40 = A[o]*e^(-0.54)}}}
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Finding {{{e^(-0.54)}}} is just a calculator exercise. On most calculators the key will
be marked {{{e^x}}}. Enter -0.54 and press the key to get 0.582748252. Substitute that
number into the equation to get:
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{{{40 = A[o]*(0.582748252)}}}
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Now solve for {{{A[o]}}} by dividing both sides of this equation by 0.582748252 to get:
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{{{A[o] = 40/0.582748252 = 68.64027449}}}
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So the answer is that you should start with 68.64027449 grams to have 40 grams left after
three days.  Note that the closest answer in your list of answers is 68.6 grams.
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Hope this work helps to get you familiar with solving exponential equations such as this.
This type of equation crops up in chemistry, physics, electronics, math, and societal studies
and you may need to understand how to handle them at some point.