a radioactive substance decays at an annual rate of 24 percent. If the initial amount of the substance is 640 grams, which of the following functions (f) models the remaining amount of the substance, in grams, t years later?
You left out your choices
amount at year n = initial amount * (.76)^n
just like compound interest but decreasing
To model the remaining amount of the radioactive substance, we can use an exponential decay function. The general form of such a function is:
f(t) = P(1 - r)^t
Where:
- f(t) represents the remaining amount of the substance after t years.
- P is the initial amount of the substance.
- r is the decay rate.
In this case, the initial amount (P) of the substance is 640 grams, and the decay rate (r) is 24 percent, or 0.24.
Plugging in the values into the formula, we have:
f(t) = 640(1 - 0.24)^t
Simplifying further:
f(t) = 640(0.76)^t
Therefore, the function that models the remaining amount of the substance (in grams) t years later is:
f(t) = 640(0.76)^t