(a) Between 2005 and 2015, ACME Widgets sold widgets at a continuous rate of R = R₀e^0.125t widgets per year, where t is time in years since January 1, 2005. Suppose they were selling widgets at a rate of 1000 per year on January 1, 2005. How many widgets did they sell between 2005 and 2015? How many did they sell if the rate on January 1, 2005 was 1,000,000 widgets per year?
(b) In the first case (1000 widgets per year on January 1, 2005), how long did it take for half the widgets in the ten-year period to be sold? In the second case (1,000,000 widgets per year on January 1, 2005), when had half the widgets in the ten-year period been sold?
(c) In 2015, ACME advertised that half the widgets it had sold in the previous ten years were still in use. Based on your answer to part (b), how long must a widget last in order to justify this claim?