Respuesta :

Answer:

After 5 minutes, it remains 75.73 grams of mass.

Step-by-step explanation:

Each minute, the mass is decreased by a 25.5%. So, we can find the mass after each minute period.

First minute.

[tex]330gr-0.255(330gr)=(330-84.15)gr=245.85 gr[/tex]

Second minute.

[tex]245.85-0.255(245.85)=245.85-62.69=183.16gr[/tex]

Third minute.

[tex]183.16-0.255(183.16)=183.16-46.70=136.45gr[/tex]

Fourth minute.

[tex]136.45-0.255(136.45)=136.45-34.80=101.65[/tex]

Fifth minute.

[tex]101.65-0.255(101.65)=101.65-25.92=75.73gr[/tex]

Therefore, after 5 minutes, it remains 75.73 grams of mass.

Using an exponential function, it is found that 75.7 grams of the element remains after 5 minutes.

What is an exponential function?

A decaying exponential function is modeled by:

[tex]A(t) = A(0)(1 - r)^t[/tex]

In which:

  • A(0) is the initial value.
  • r is the decay rate, as a decimal.

In this problem:

  • The element has mass of 330 grams, hence A(0) = 330.
  • It decays by 25.5% per minute, hence r = 0.255.

Then, the equation is:

[tex]A(t) = A(0)(1 - r)^t[/tex]

[tex]A(t) = 330(1 - 0.255)^t[/tex]

[tex]A(t) = 330(0.745)^t[/tex]

After 5 minutes, we have that t = 5, hence the amount is:

[tex]A(t) = 330(0.745)^5 = 75.7[/tex]

75.7 grams of the element remains after 5 minutes.

You can learn more about exponential functions at https://brainly.com/question/25537936

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