Question

A certain element has a half life of 4.5 billion years.

Answer 1

A ) 50% is gone so 4.5 billion right of the bat. Then another 4.5 if it got down to 25% but it’s still at 35%. So it lost 15% from 50%. 15/25 * 4.5 billion = 2.7 billion +the original 4.5 = 7.2 billion years old.

B) it loses 45%. 50% would be 4.5 billion. 45/50 * 4.5 billion = 4.05 billion years old

Answer 2

Answer:

Step-by-step explanation:

Given that a  certain element has a half life of 4.5 billion years.

For half life of 4.5 billion years we have the equation as

$P(t) = P_0(t)(\frac{1}{2} )^{\frac{t}{t_{1/2} } }$

=$P_0(t)(\frac{1}{2} )^{\frac{t}{4.5} } }$ where t is in billions of years.

When P(t) = 35% of original we have

$P(t) = 0.35 P_0(t) = P_0(t)(\frac{1}{2} )^{\frac{t}{t_{1/2} } }\\0.35 = (\frac{1}{2} )^{\frac{t}{4.5} } }\\ln0.35 = {\frac{t}{4.5} }ln (\frac{1}{2} \\t =6.816$

After 6.816 billion years.

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b) Here $P(t) = 0.55 P_o(t)$

$t = \frac{log 0.55}{log 0.5} (4.5)\\t=3.88$

After 3.88 billion years.