Question

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

Answer 1

Answer:

$M(t) = 175(0.9943)^{t}$

Step-by-step explanation:

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

$M(t) = ab^{t}$

In which a is the initial amount.

175g sample:

This means that $a = 175$

So

$M(t) = 175b^{t}$

Half-life of 122 days.

This means that $M(122) = 0.5*175 = 87.5$

So

$M(t) = 175b^{t}$

$87.5 = 175b^{122}$

$b^{122} = 0.5$

$\sqrt[122]{b^{122}} = \sqrt[122]{0.5}$

$b = 0.9943$

So

$M(t) = 175(0.9943)^{t}$