contestada

A scientist is studying the relationship of two quantities S and T in an experiment. The scientist finds that
under certain conditions, as the quantity of S increases, the quantity of T decreases. After taking
measurements, the scientist determines that the rate of change of the quantity of S with respect to the
quantity of T present is inversely proportional to the natural logarithm of the quantity of T. Which of the
following is a differential equation that could describe this relationship?

Respuesta :

Differential equation is a way to represents the function and its variable by relating them.Hence the differential equation that describe the relationship between S and T is,

[tex]S \propto \dfrac{1}{log_e T}[/tex]

Given-

The quantity of S increases, the quantity of T decreases.

The rate of change of the quantity of S with respect to the  quantity of T present is inversely proportional to the natural logarithm of the quantity of T.

What is differential equation?

Differential equation is a way to represents the function and its variable by relating them.

As the quantity of S changes with respect to the  quantity of T present is inversely proportional. Thus,

[tex]S \propto \dfrac{1}{T}[/tex]

But quantity of S changes inversely proportional to the natural logarithm of the quantity of T. The natural logarithm of a  number is its logarithm to the base of e (constant).

Thus the equation can be given is,

[tex]S \propto \dfrac{1}{log_e T}[/tex]

Hence the differential equation that describe the relationship between S and T is,

[tex]S \propto \dfrac{1}{log_e T}[/tex]

Learn more about the differential equation here;

https://brainly.com/question/25731911

Otras preguntas