No. 1 JUNE, 1938 25. Superman comic book. In August 2014, a 1938 comic book featuring...

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No. 1 JUNE, 1938 25. Superman comic book. In August 2014, a 1938 comic book featuring the first appearance of Superman sold at auction for a record price of $3.2 million. The comic book originally cost 10 ($0.10). (Sources: eBay; money .cnn.com.) Use the two data points (0, $0.10) and (76, $3,200,000), and assume that the value V of the comic book has grown expo- nentially, as given by dv dt = kV. (In the summer of 2010, a family faced foreclo- sure on their mortgage. As they were packing, they came across some old comic books in the basement, and one of CTION COMICS 10 them was a copy of this first Superman comic. They sold it and saved their house.) a) Find the function that satisfies this equation. Assume that Vo $0.10 and t is the number of years after 1938. b) Estimate the value of the comic book in 2020. c) After what time will the value of the comic book be $30 million, assuming there is no change in the growth rate? No. 1 JUNE, 1938 25. Superman comic book. In August 2014, a 1938 comic book featuring the first appearance of Superman sold at auction for a record price of $3.2 million. The comic book originally cost 10 ($0.10). (Sources: eBay; money .cnn.com.) Use the two data points (0, $0.10) and (76, $3,200,000), and assume that the value V of the comic book has grown expo- nentially, as given by dv dt = kV. (In the summer of 2010, a family faced foreclo- sure on their mortgage. As they were packing, they came across some old comic books in the basement, and one of CTION COMICS 10 them was a copy of this first Superman comic. They sold it and saved their house.) a) Find the function that satisfies this equation. Assume that Vo $0.10 and t is the number of years after 1938. b) Estimate the value of the comic book in 2020. c) After what time will the value of the comic book be $30 million, assuming there is no change in the growth rate?