Question

experiment (S1): ideal environment In the first test, a culture medium for bacteria was generated where the ideal temperature for their reproduction cycle was maintained. This allowed us to accurately predict the quantity of bacteria after having gone through a division process, through an expotential model defined as follows: S1 (x) = 4 * C ^ 0.57x + 3 Where x corresponds to the hours elapsed since the start of the experiment and S1 the number of bacteria at this moment. What was the initial amount of bacteria in the experiment?

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Fred

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1. Evaluamos la función en x = 0 ya que queremos conocer la cantidad inicial de bacterias.

2. Sustituimosx = 0 en la función S1(x) = 4C^{0.57x} + 3 , obteniendo S1(0) = 4C^{0.57 \times 0} + 3 .

3. Simplificamos el exponente:0.57 \times 0 = 0 por lo que tenemos 4C^0 + 3 .

4. Usamos la propiedad de los exponentes, donde cualquier número a la potencia de 0 es 1:C^0 = 1 .

5. Entonces, la ecuación se simplifica a4 \cdot 1 + 3 = 4 + 3 = 7 .

6. Por lo tanto, la cantidad inicial de bacterias es7 .

2. Sustituimos

3. Simplificamos el exponente:

4. Usamos la propiedad de los exponentes, donde cualquier número a la potencia de 0 es 1:

5. Entonces, la ecuación se simplifica a

6. Por lo tanto, la cantidad inicial de bacterias es

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