Answer:
[tex]y=500\cdot 0.658^{\frac{x}{2}}[/tex]
Step-by-step explanation:
Express the weight as the exponential function of months
[tex]y=a\cdot b^{\frac{x}{2}}[/tex]
When [tex]x=0,[/tex] then
[tex]500=a\cdot b^{\frac{0}{2}}\\ \\500=a\cdot b^0\\ \\500=a[/tex]
Hence,
[tex]y=500\cdot b^{\frac{x}{2}}[/tex]
When [tex]x=2,[/tex] then
[tex]329=500\cdot b^{\frac{2}{2}}\\ \\329=500b^1\\ \\329=500b\\ \\b=\dfrac{329}{500}=0.658[/tex]
Therefore,
[tex]y=500\cdot 0.658^{\frac{x}{2}}[/tex]
Check the rest values:
[tex]x=4: \ y=500\cdot 0.658^{\frac{4}{2}}=500\cdot 0.658^2\approx 216\\ \\x=6:\ y=500\cdot 0.658^{\frac{6}{2}}=500\cdot 0.658^3\approx 142\\ \\x=8:\ y=500\cdot 0.658^{\frac{8}{2}}=500\cdot 0.658^4\approx 93\\ \\x=10:\ y=500\cdot 0.658^{\frac{10}{2}}=500\cdot 0.658^5\approx 61\\ \\x=12:\ y=500\cdot 0.658^{\frac{12}{2}}=500\cdot 0.658^6\approx 40[/tex]
