Question

Hi Guys, trying to figure out a exponential growth problem. I have to complete the table
t (yrs) 0 ? ? ?
N (g) 10 5 2.5 1.25
The half life of the substance is 4.9 x 10^9 years.
I'm not sure how to setup the equation
1/2No = Noe ^kt to get each half life value? (which are what the question marks stand for in the table).. Anyone might be able to help, greatly appreciate it.

Answer 1

I'm really only trying to figure out the half life because if I multiply it out it comes out to like 9 trillion or something like that so I'm assuming there has to be another way of finding the half life for the table instead of putting 0 then 9000000000000000 then 1800000000000000 and so on...

Answer 2

Why are you using all those zeros? That's why we invented "Scientific Notation".

You have \(N_{0} = 10\) and t = 4.9 x 10^9 years to achieve 5 (half the original)

You really don't need a lot of arithmetic on this one. Notice how 5 is half of 10, then 2.5 is half of 5, and finally 1.25 is half of 2.5? This is just three half-life periods.

Your question marks are simple.

4.9 * 10^9
9.8 * 10^9
1.47 * 10^10

Just add 4.9*10^9 for each half-life period.

Answer 3

Ohh. ok. Thank you yes I didn't understand I could write the time value as a exponential number I thought it had to be the actual years multiplied out..