To find out how much of the substance will be left after 5 years, we can use the given formula A = Aâe^(kt).
Given:
Initial amount of substance, Aâ = 20g
Time, t = 5 years
Half-life, tâ/â = 10 years
First, let's find the value of the constant k using the half-life formula.
The half-life formula is:
tâ/â = (ln 2) / k
Substituting the given half-life, we get:
10 = (ln 2) / k
To solve for k, we can rearrange the equation as:
k = (ln 2) / 10
Now that we have the value of k, we can substitute it and the given values into the formula A = Aâe^(kt).
A = 20 * e^((ln 2/10) * 5)
Let's calculate the expression inside the exponential first, (ln 2/10) * 5:
(ln 2/10) * 5 â 0.115
Then, we can continue with the equation:
A = 20 * e^0.115
Using a calculator or computer, we can evaluate e^0.115 to be approximately 1.122.
Therefore,
A â 20 * 1.122 â 22.44
After 5 years, approximately 22.44g of the substance will be left.