Question

the number of kilograms, y, of a radioactive element that remains that after t hours can be modeled by the equation y=0.23(0.91)t what is the rate of decrease of this radioactive element?

Answer 1

0.2093

Step-by-step explanation:

Given that after $t$ hours,the number of kilograms $y$ of the radio active material is 0.23(0.91)t

$y=0.23(0.91)t$

rate of decrease of this radio active element=$\frac{dy}{dt}$

$\frac{dy}{dt}$ represents the slope of the graph $y\text{ vs }t$

Slope is $\frac{y_{2}-y_{1}}{t_{2}-t_{1}}$,which is the rate at which $y$ decreases with time.

$\frac{dkt}{dt}=k$ for constant k

calculate $y\text{ vs }t$ =$\frac{d(0.23(0.91)t)}{dt} =0.2093$