Answer: Check explanation.
Explanation:
Important things to note from the question: the total number the bacteria stated with is =460. After time(t), which is two hours passed, the numbers of bacteria increased to= 920.
Now, let us delve into the solution.
The number of bacteria at any time,t= N(t). And N(t) = e^Xt + V. Where V = ln 460 and X can be calculated below;
total number of bacteria remaining after the two hours, 920 = e^2X. e^460.
So, we make Exponential 2X the subject of the formula;
Therefore, e^2X = 920/460.
====> e^2X = 2.
The exponential goes into the right side, turns into 'ln'.
====> 2X = ln 2.
Therefore, X= 1/2 ×ln 2.
OR
X= 0.5 × 0.69315 = 0.35.
Therefore, Expressing the population after t hours as a function of t;
N(t) = 460 × (e^1/2 ln 2)t.
OR
N(t)= 460× e^0.35 t.
CONCLUSION: With this we can slot in any value of time,t to determine the value of the number of bacteria at any time,t(N)
