contestada

2. A 175g sample of radioactive kryptonite-344 has a half-life of 122 days.

a) Write the exponential equation that gives the amount of kryptonite that remains after t days.

Write equation in the form M(t)= ab* where x=

elapsed time

half-life time

Respuesta :

Answer:

[tex]M(t) = 175(0.9943)^{t}[/tex]

Step-by-step explanation:

The amount of kryptonite-344 after t days is given by the following equation:

[tex]M(t) = ab^{t}[/tex]

In which a is the initial amount.

175g sample:

This means that [tex]a = 175[/tex]

So

[tex]M(t) = 175b^{t}[/tex]

Half-life of 122 days.

This means that [tex]M(122) = 0.5*175 = 87.5[/tex]

So

[tex]M(t) = 175b^{t}[/tex]

[tex]87.5 = 175b^{122}[/tex]

[tex]b^{122} = 0.5[/tex]

[tex]\sqrt[122]{b^{122}} = \sqrt[122]{0.5}[/tex]

[tex]b = 0.9943[/tex]

So

[tex]M(t) = 175(0.9943)^{t}[/tex]

Otras preguntas