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Answer:
<em>M(13)=14.3 gram</em>
Step-by-step explanation:
<u>Exponential Decay Function</u>
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](https://tex.z-dn.net/?f=C%28t%29%3DC_o%5Ccdot%281-r%29%5Et)
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](https://tex.z-dn.net/?f=M%28t%29%3DM_o%5Ccdot%281-r%29%5Et)
![M(t)=970\cdot(1-0.277)^t](https://tex.z-dn.net/?f=M%28t%29%3D970%5Ccdot%281-0.277%29%5Et)
Operating:
![M(t)=970\cdot 0.723^t](https://tex.z-dn.net/?f=M%28t%29%3D970%5Ccdot%200.723%5Et)
After t=13 minutes the remaining mass is:
![M(13)=970\cdot 0.723^{13}](https://tex.z-dn.net/?f=M%2813%29%3D970%5Ccdot%200.723%5E%7B13%7D)
Calculating:
M(13)=14.3 gram
Answer:
y-6 = -7x + 21
Step-by-step explanation:
Find the slope
(-8 - 6)/(5-3)
-14/2 = -7
Now find the formula
y-6=-7(x - 3)
y-6 = -7x + 21
Another way to write it is
y= -7x + 27
Answer: 1574
Step-by-step explanation:
1345 plus 116 equals 1461
1461 plus 113 equals 1574
Answer:
D. -1/2
Step-by-step explanation:
When a line is perpendicular to another line the slope will be the exact opposite. For example line A = y = 3x + 5 the line perpendicular to it will be -1/3x.
So -1/2 is the slope of your perpendicular line.