Thorium -228 is a radioactive substance that decays 50% every 1.9 years. how much of a 50 gram sample will exist after 22.8 years? round to 3 decimal places. use the formula a=a0e^ -kt.
a.) 19.34 grams
b.) 30.32 grams
c.) 0.124 grams
d.) 12.4 grams
e.) 7.48 grams

Step-by-step explanation:

The exponential decrease formula that we must use is:

Where A is the amount of thorium as a function of time

is the initial amount and k is the decrease rate

We know that initially there are 50 gr and that you decay 50% every 1.9 years.

So

We solve the equation for k

After 22.8 years the amount of thorium that exists is:

the correct answer is option c.   3

step-by-step explanation:

points to remember

equation of the line with coordinates (x₁, y₁) and (x₂, y₂) is given by,

slope m = (y₂ - y₁)/(x₂ - x₁)

from the figure we can see a line with two coordinates given

to find the slope of given line

here   (x₁, y₁)   = (-1, -1 ) and (x₂, y₂) = (1, 5)

slope m = (y₂ - y₁)/(x₂ - x₁)

  = (5 - -1)/(1 - -1)

  = (5 + 1)/(1 + 1)

  = 6/2 = 3

therefore the correct answer is option c.   3