The half-life of Palladium-100 is 4 days. A lab is working with a sample of with 3250mg. Write a function, f(x), to represent the amount of Palladium-100 left after x days
f(x) = 3250*(1/2)^(x/4)
To write the function f(x) to represent the amount of Palladium-100 left after x days, we need to use the formula for exponential decay.
The formula for the amount remaining after a certain time using the half-life is:
A = A₀ * 0.5^(t / h),
where A is the final amount, A₀ is the initial amount, t is the time passed, and h is the half-life.
In this case, the initial amount A₀ is 3250mg, the time passed t is x days, and the half-life h is 4 days.
Substituting these values into the formula, we get:
f(x) = 3250 * 0.5^(x / 4).
Therefore, the function f(x) to represent the amount of Palladium-100 left after x days is f(x) = 3250 * 0.5^(x / 4).