Question

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

Answer 1

Answer:

$y=500\cdot 0.658^{\frac{x}{2}}$

Step-by-step explanation:

Express the weight as the exponential function of months

$y=a\cdot b^{\frac{x}{2}}$

When $x=0,$ then

$500=a\cdot b^{\frac{0}{2}}\\ \\500=a\cdot b^0\\ \\500=a$

Hence,

$y=500\cdot b^{\frac{x}{2}}$

When $x=2,$ then

$329=500\cdot b^{\frac{2}{2}}\\ \\329=500b^1\\ \\329=500b\\ \\b=\dfrac{329}{500}=0.658$

Therefore,

$y=500\cdot 0.658^{\frac{x}{2}}$

Check the rest values:

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