Answer:
M(13)=14.3 gram
Step-by-step explanation:
Exponential Decay Function
The exponential function is used to model natural decaying processes, where the change is proportional to the actual quantity.
An exponential decaying function is expressed as:
[tex]C(t)=C_o\cdot(1-r)^t[/tex]
Where:
C(t) is the actual value of the function at time t
Co is the initial value of C at t=0
r is the decaying rate, expressed in decimal
The element has an initial mass of Mo=970 grams, the decaying rate is r=27.7% = 0.277 per minute.
The equation of the model is:
[tex]M(t)=M_o\cdot(1-r)^t[/tex]
[tex]M(t)=970\cdot(1-0.277)^t[/tex]
Operating:
[tex]M(t)=970\cdot 0.723^t[/tex]
After t=13 minutes the remaining mass is:
[tex]M(13)=970\cdot 0.723^{13}[/tex]
Calculating:
M(13)=14.3 gram
