Respuesta :
Answer:
The function that represents the mass of the sample after t days is [tex]A(t) = 390(0.41)^t[/tex].
The percentage rate of change per hour is of -2.46%.
Step-by-step explanation:
Exponential amount of decay:
The exponential amount of decay for an amount of a substance after t days is given by:
[tex]A(t) = A(0)(1-r)^t[/tex]
In which A(0) is the initial amount, and r is the decay rate, as a decimal.
Element X is a radioactive isotope such that its mass decreases by 59% every day. The experiments starts out with 390 grams of Element X.
This means, respectively, that [tex]r = 0.59, A(0) = 390[/tex]
So
[tex]A(t) = A(0)(1-r)^t[/tex]
[tex]A(t) = 390(1-0.59)^t[/tex]
[tex]A(t) = 390(0.41)^t[/tex]
The function that represents the mass of the sample after t days is [tex]A(t) = 390(0.41)^t[/tex].
Hourly rate of change:
Decreases by 59% every day, which means that for 24 hours, the rate of change is of -59%. So
-59%/24 = -2.46%
The percentage rate of change per hour is of -2.46%.
