Questions: The age/weight relationship of a particular animal can be estimated by the function M(t)=3105 e^(-e^(-0.021(t-53))), where t is the age of this animal in days and M(t) is the weight of this animal in grams. a. Estimate the weight of an animal that is 200 days old. The animal weighs approximately grams when it is 200 days old. (Round to two decimal places as needed.)

Solution Steps

To estimate the weight of an animal that is 200 days old using the given function \( M(t) = 3105 e^{-e^{-0.021(t-53)}} \), we need to substitute \( t = 200 \) into the function and evaluate it.

The weight of the animal as a function of its age in days is given by: \[ M(t) = 3105 e^{-e^{-0.021(t-53)}} \]

Substitute \( t = 200 \) into the function: \[ M(200) = 3105 e^{-e^{-0.021(200-53)}} \]

Calculate the exponent: \[ -0.021(200 - 53) = -0.021 \times 147 = -3.087 \]

Evaluate the inner exponential: \[ e^{-3.087} \approx 0.0456 \]

Evaluate the outer exponential: \[ e^{-0.0456} \approx 0.9554 \]

Multiply by 3105 to find the weight: \[ M(200) = 3105 \times 0.9554 \approx 2966.48 \]

Final Answer