Yea this question is difficult for me ive been trying to answer this for 40 mins

it is difficult

my best answer would be a. 6

hope its right!!

Explanation:

The half-life formula is

y = A*(1/2)^(x/H)

where A is the starting amount, H is the half-life, x is the time value and y is the amount after x units of time have passed.

I'll express the x and H values in terms of millions of years. So for example, when we say H = 500, then that really refers to 500 million years.

In this case, we know that,

Let's use those values to solve for x. We'll need logs to cut the exponents down from the trees.

y = A*(1/2)^(x/H)

3 = 192*(1/2)^(x/500)

3/192 = (0.5)^(x/500)

0.015625 = (0.5)^(x/500)

log(0.015625) = log( (0.5)^(x/500) )

log(0.015625) = (x/500)*log(0.5)

(x/500)*log(0.5) = log(0.015625)

x = 500*log(0.015625)/log(0.5)

x = 3,000

Keep in mind that x is in millions of years. So saying x = 3,000 means 3,000 million years. This translates to 3,000*10^6 = 3,000,000,000 = 3 billion years.

It will take about 3 billion years for the 192 atoms to decay to only 3 atoms.

The amount of half-lives this occurs is x/H = (3,000)/500 = 6

So the time span of 3 billion years is the same as 6 half-lives when each half-life is 500 million years long.