a certain element has a half - life of 69 years. an experiment starts with 1,500 grams of the element. the…

a certain element has a half - life of 69 years. an experiment starts with 1,500 grams of the element. the amount of the element remaining x years after the experiment began can be modeled with the function f(x)=1,500(2)^(-x/69). the mathematical domain of the function is all real numbers. which statement describes how the reasonable domain compares to the mathematical domain? the reasonable domain is restricted to integers. the reasonable domain is restricted to positive real numbers. the reasonable domain has a minimum value of 1,500. the reasonable domain has a maximum value of 1,500.

a certain element has a half - life of 69 years. an experiment starts with 1,500 grams of the element. the amount of the element remaining x years after the experiment began can be modeled with the function f(x)=1,500(2)^(-x/69). the mathematical domain of the function is all real numbers. which statement describes how the reasonable domain compares to the mathematical domain? the reasonable domain is restricted to integers. the reasonable domain is restricted to positive real numbers. the reasonable domain has a minimum value of 1,500. the reasonable domain has a maximum value of 1,500.

Answer

Answer:

The reasonable domain is restricted to positive real numbers.

Explanation:

Step1: Comprender el contexto

El problema se refiere a un experimento con un elemento que tiene un decaimiento exponencial.

Step2: Analizar el dominio matemático

El dominio matemático de la función $f(x)=1500(2)^{-\frac{x}{69}}$ es todos los números reales. Pero en el contexto real del experimento:

Step3: Considerar el sentido real

El tiempo $x$ (años después del comienzo del experimento) no puede ser negativo, ya que no podemos tener tiempo retroactivo en este experimento. Además, puede ser cualquier valor positivo real (pueden ser fracciones de años), no solo números enteros. Y el valor 1500 se refiere a la cantidad inicial del elemento, no al dominio. Entonces, el dominio razonable está restringido a números reales positivos.