Question

Algebra 2 (picture shown)

Answer 1

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:

$C(t)=C_o\cdot(1-r)^t$

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:

$M(t)=M_o\cdot(1-r)^t$

$M(t)=970\cdot(1-0.277)^t$

Operating:

$M(t)=970\cdot 0.723^t$

After t=13 minutes the remaining mass is:

$M(13)=970\cdot 0.723^{13}$

Calculating:

M(13)=14.3 gram