Mathematics: 100 point giveaway get it when you can

100 point giveaway get it when you can - id10014972891, kenna1323

LulPink

03.11.2022

t = 15825.11 years

Step-by-step explanation:

From the given information:

We can make use of the activity of the sample present after time "t" to determine the age of the sample.

This can be expressed by the formula:

$A = A_o e^{-\lambda t}$ --- (1)

where;

A_o = activity of the sample at time t = 0

$\lambda$ = disintegration constant

$\lambda = \dfrac{0.693}{T_{1/2}}$

If we replace the value of $\lambda$ into equation (1), we have:

$A = A_o e^{ \Bigg [ -{ \dfrac{0.693}{T_{1/2}} \Bigg ] } t}$

$\dfrac{A}{A_o} = e^{ \Bigg [ -{ \dfrac{0.693}{T_{1/2}} \Bigg ] } t}$

By rearrangement:

$t = \dfrac{-T_{1/2} In (\dfrac{A}{A_o})}{0.693}$

$t = - \dfrac{\left(5730\ \cdot\ \ln\left(\frac{\left(1770\right)}{0.8\cdot10^{3}\cdot15}\right)\right)}{0.693}$

t = 15825.11 years

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