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)to the 1st power. What is the rate of decrease of this radioactive element?

Answer 1

Answer:

The rate of decrease is 8%

Step-by-step explanation:

we know that

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

$a=a_0(1-r)^t$

where

a is the amount in kilograms after time t.

a_0 is the original amount of the substance or y-intercept of the function

r is the decay rate, written in decimals.

t is the time

In this problem we have

$a=0.65(0.92)^t$

so

$a_0=0.65\\(1-r)=0.92$

solve for r

$r=1-0.92=0.08$

Convert to percentage

$0.08(100)=8\%$