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I am having a hard time figuring this out can some one please help!1

As a scientist, you study 200 grams of radioactive material for several months and you have obtained the following data:

Month, Weight

0, 500
2, 329
4, 216.1
6, 142
8, 93
10, 61.29
12, 40.3
Express the weight as the function of months.

User Zhen Sun
by
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1 Answer

5 votes

Answer:


y=500\cdot 0.658^{(x)/(2)}

Explanation:

Express the weight as the exponential function of months


y=a\cdot b^{(x)/(2)}

When
x=0, then


500=a\cdot b^{(0)/(2)}\\ \\500=a\cdot b^0\\ \\500=a

Hence,


y=500\cdot b^{(x)/(2)}

When
x=2, then


329=500\cdot b^{(2)/(2)}\\ \\329=500b^1\\ \\329=500b\\ \\b=(329)/(500)=0.658

Therefore,


y=500\cdot 0.658^{(x)/(2)}

Check the rest values:


x=4: \ y=500\cdot 0.658^{(4)/(2)}=500\cdot 0.658^2\approx 216\\ \\x=6:\ y=500\cdot 0.658^{(6)/(2)}=500\cdot 0.658^3\approx 142\\ \\x=8:\ y=500\cdot 0.658^{(8)/(2)}=500\cdot 0.658^4\approx 93\\ \\x=10:\ y=500\cdot 0.658^{(10)/(2)}=500\cdot 0.658^5\approx 61\\ \\x=12:\ y=500\cdot 0.658^{(12)/(2)}=500\cdot 0.658^6\approx 40

User Thaddee Tyl
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