Question

The amount in kilograms a, of a radioactive element that remains after t hours can be modeled by the equation a=0.65(0.92)t. What is the rate of decrease of this radioactive element

Answer 1

The given equation is:


`a=0.65(0.92)^(t)`

The general equation for the radioactive decay can be written as:


`a= a_(0)(1-r)^(t)`

Where,
a₀ is the original amount of the substance
a is the amount after time t.
r is the decay rate, written in decimals.
t is the time.

Transforming the given equation, we can write:


`a=0.65(1-0.08)^(t)`

This means the decay rate for this radioactive element is 0.08 = 8%

Thus the percentage of decrease of the given radioactive element is 8%