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The value of a new boat depreciates after it is purchased. The value of the boat 7 years after it was purchased is $25,000 and its value has been decreasing at the rate of 8.2% per year.
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Find the initial value of the boat when it was purchased.
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How many years after it was purchased will the boat’s value be $20,000?
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What was its value 3 years after the boat was purchased?
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Tony invested $40,000 in 2010; unfortunately his investment has been losing value at the rate of 2.7% per year.
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Write the function that gives the value of the investment as a function of time \(t\) in years after 2010.
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Find the value of the investment in 2020, if its value continues to decrease at this rate.
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In what year will the investment be worth half its original value?
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Rosa invested $25,000 in 2005; its value has been increasing at the rate of 6.4% annually.
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Write the function that gives the value of the investment as a function of time \(t\) in years after 2005.
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Find the value of the investment in 2025.
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The population of a city is increasing at the rate of 3.2% per year, since the year 2000. Its population in 2015 was 235,000 people.
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Find the population of the city in the year 2000.
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In what year with the population be 250, 000 if it continues to grow at this rate.
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What was the population of this city in the year 2008?
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The population of an endangered species has only 5000 animals now. Its population has been decreasing at the rate of 12% per year.
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If the population continues to decrease at this rate, how many animals will be in this population 4 years from now.
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In what year will there be only 2000 animals remaining in this population?
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300 mg of a medication is administered to a patient. After 5 hours, only 80 mg remains in the bloodstream.
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Using an exponential decay model, find the hourly decay rate.
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How many hours after the 300 mg dose of medication was administered was there 125 mg in the bloodstream
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How much medication remains in the bloodstream after 8 hours?
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If \(y = 240b^t\) and \(y = 600\) when \(t = 6\) years, find the annual growth rate. State your answer as a percent.
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If the function is given in the form \(y = ae^{kt}\), rewrite it in the form \(y = ab^t\).
If the function is given in the form \(y = ab^t\), rewrite it in the form \(y = ae^{kt}\).
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\(y=375000\left(1.125^{t}\right) \nonumber\)
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\(y=5400 e^{0.127 t} \nonumber \)
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\(y=230 e^{-0.62 t}\)
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\(y=3600\left(0.42^{t}\right)\)