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

Answer: (C)

19

Answer 2

Starting with 2 organisms on day-1, each day the population grows.
On day-2, it's 2 2 + 3 = 7, and on day-3, it's 2 7 + 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.