The following table shows the number of drug overdose deaths involving nonprescription synthetic narcotics (primarily fentanyl) in recent years.

(a) Letting t represent the years since 2010, find a function of the form y = y₀e^kt that fits the data at 2011 and 2016.
(b) If you have a graphing calculator or computer program with an exponential regression feature, find an exponential growth function that best fits the data.
(c) Use a graphing calculator to plot the data and your functions from parts (a) and (b).
(d) Predict the number number of drug overdose deaths involving nonprescription synthetic narcotics in the year 2025 based on the functions from parts (a) and (b). Which prediction, if either, is more realistic?

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Year 2011 2012 2013 2014 2015 2016 2017 Deaths 2666 2628 3105 5544 9580 19,413 28,466