If a scientist puts one hundred bacteria into a petri dish at time t=0. Five hours later she measures 330 bacteria. Assuming exponential growth, the growth constant, k, for the bacteria, is approximately 0.2706.
To calculate the growth constant, k, for the bacteria, we'll use the exponential growth formula:
N(t) = Nā x e(kt)
Where N(t) is the number of bacteria at time t, Nā is the initial number of bacteria, k is the growth constant, and t is time in hours. We know that Nā = 100, N(t) = 330, and t = 5 hours.
330 = 100 x e(5k)
Now, we'll solve for k:
1. Divide both sides by 100:
3.3 = e(5k)
2. Take the natural logarithm (ln) of both sides:
ln(3.3) = 5k
3. Divide by 5 to find k:
k = ln(3.3)/5 ā 0.2706
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