y=y0e−kt ...(i)
Here, y is the amount of element at time t, yo is the initial amount, k is decay constant.
Given, y0=700 gm.
When t=24000,y=21y0
Putting all these values in (i).
y=y0e−kt⇒21y0=y0e−k(24000)⇒21=e−24000k⇒ln21=−24000k⇒k≈0.00002888113
So, y=700e−0.00002888113t
Now, y=0.78(700),t=?
0.78(700)=700e−0.00002888113t⇒0.78=e−0.00002888113t⇒ln0.78=−0.00002888113t⇒t≈8603
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