Question

The half life of a Rock is: 6.7 Billion years
Amount Element: 10%
Amount lead: 90%
Age of Rock: ?

Can someone please help?

Answer 1

90% lead tells us that 90% of the rock has been decayed so far

Answer 2

ok.

Answer 3

Half life of 6.7 billion years tells us that half of the stuff gets decayed every 6.7 billion years :
\[Q' = Q*\left(\dfrac{1}{2}\right)^{t/6.7}\]

Observe that when t = 6.7 in above equation, you do get Q' = Q/2 as expected

Answer 4

What does Q represent?

Answer 5

Q is the starting `amount of substance`

Q' is the substance remaining after `t` billion years

Answer 6

Simply replace Q' by 0.1Q and solve t

Answer 7

\[0.1Q = Q*\left(\dfrac{1}{2}\right)^{t/6.7}\]

Answer 8

Can you please show me the process im still confused.

Answer 9

Start by cancelling Q both sides

Answer 10

ok

Answer 11

\[0.1 = \left(\dfrac{1}{2}\right)^{t/6.7}\]


Your goal is to isolate \(t\)

Answer 12

How good are you with logarithms ?

Answer 13

not good at all

Answer 14

Thank you so much for your help

Answer 15

This is the best example to make sense of logarithms too

Answer 16

Let me introduce you to logarithms quick.

Look at the expression \(2^3 = 8\).
Is it a true statement ?

Answer 17

hmm

Answer 18

yes

Answer 19

Focus on the exponent. The thing on the top : 3.

Answer 20

\(2^3 = 8\)

We say \(3\) is the logarithm of 8 when base is 2.

Answer 21

As you can see, logarithm = exponent

Answer 22

Look at \(10^4 = 1000\)
What is the logarithm of 1000 in base 10 ?

Answer 23

oh ok its starting to make scense

Answer 24

\[10^3?\]

Answer 25

Careful, logarithm = exponent

Answer 26

Only exponent

Answer 27

Expressed mathematically, this might be a bit helpful