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 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
Updated On: Jan 13, 2026
- 15
- 17
- 19
- 23
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The Correct Option is C
Solution and Explanation
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) = 2π + 3(2πβ1β1).
To find when the population exceeds 1 million,
we check for n = 19, where we get 219 + 3(218β1) = 220 + 218β3,
which is indeed over a million. For n = 18, it's 218 + 3(217β1) = 219 + 217β3,
which is not over a million.
So, the population surpasses a million at n = 19.
On day-2, it's 22 + 3 = 7, and on day-3, it's 27 + 3 = 17.
Following the pattern, we see T(n) = 2π + 3(2πβ1β1).
To find when the population exceeds 1 million,
we check for n = 19, where we get 219 + 3(218β1) = 220 + 218β3,
which is indeed over a million. For n = 18, it's 218 + 3(217β1) = 219 + 217β3,
which is not over a million.
So, the population surpasses a million at n = 19.
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