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

Starting with 2 organisms on day-1, each day the population grows. 
On day-2, it's 22 + 3 = 7, and on day-3, it's 27 + 3 = 17. 
Following the pattern, we see T(n) = 2𝑛 + 3(2𝑛−1−1).
To find when the population exceeds 1 million, 
we check for n = 19, where we get 2¹⁹ + 3(2¹⁸−1) = 2²⁰ + 2¹⁸−3, 
which is indeed over a million. For n = 18, it's 2¹⁸ + 3(2¹⁷−1) = 2¹⁹ + 2¹⁷−3, 
which is not over a million. 
So, the population surpasses a million at n = 19.