Question

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

• A. 15
• B. 17
• C. 19
• D. 23

Answer 1

The Correct Option is C

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.