A lab experiment measures the number of organisms at 8 am every day. Starting with 2 organisms on the first day, the number of organisms on any day is equal to 3 more than twice the number on the previous day. If the number of organisms on the nth day exceeds one million, then the lowest possible value of n is

Question

Two boats met at a point and one of them moves towards West while one towards South. After 2 hours, distance between them is 60 km. Find the speed of the slower boat if the difference in two speeds is 6 kmph.

Answer 1

The organism population begins with 2 individuals on day-1 and increases daily. On day-2, the population is 2(2) + 3 = 7. On day-3, it becomes 2(7) + 3 = 17. The growth pattern is described by the formula T(n) = 2n + 3(2^n-1-1). To determine when the population exceeds 1 million, we examine day 19. At n = 19, the population is 2¹⁹ + 3(2¹⁸-1) = 2²⁰+ 2¹⁸−3, which is greater than one million. For day 18 (n = 18), the population is 2¹⁸ + 3(2¹⁷-1) = 2¹⁹+ 2¹⁷−3, which is less than one million. Therefore, the population surpasses one million on day 19.

The Correct Option is C

Solution and Explanation

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