Question

Algebra 2 (picture shown)

Answer 1

M(13)=14.3 gram

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