Solve the problem.
-A bacteria colony doubles in 5 hr. How long does it take the colony to triple? Use N $$\mathrm { N } = \mathrm { N } _ { 0 } 2 ^ { \mathrm { t } / \mathrm { T } }$$ , where N0 is the initial number of bacteria and T is the time in hours it takes the colony to double. (Round to the nearest
Hundredth, as necessary.)
A) 7.5 hr
B) 15 hr
C) 7.92 hr
D) 2.03 hr

Question

Quizplus · Accepted Answer

If the colony doubles in 5 hours, we can use the formula to find the growth rate: 
N = N0 * 2^(t/T) 
where N0 is the initial number of bacteria, t is the time elapsed, and T is the time it takes for the colony to double.
Let N0 = 1 (for simplicity)
If the colony doubles in 5 hours, then T = 5.
So, after t hours, the number of bacteria is: 
N = 1 * 2^(t/5)
To find the time it takes for the colony to triple, we need to solve for t when N = 3: 
3 = 1 * 2^(t/5) 
2^(t/5) = 3 
t/5 = log2(3) 
t = 5*log2(3)
t ≈ 7.92 hours 
Therefore, the answer is C.

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