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Advanced Math / Nonlinear functions Difficulty: Medium

$m (t) = - 0.0274 {(\frac{t}{7})}^{2} + 7.3873 (\frac{t}{7}) + 75.032$

The function $m$ gives the predicted body mass $m (t)$ , in $kilograms (kg)$ , of a certain animal $t$ days after it was born in a wildlife reserve, where $t less than or equals 390$ . Which of the following is the best interpretation of the statement “ $m left parenthesis 330 right parenthesis$ is approximately equal to $362$ ” in this context?

The predicted body mass of the animal was approximately $330 kg$ $362$ days after it was born.

The predicted body mass of the animal was approximately $362 kg$ $330$ days after it was born.

The predicted body mass of the animal was approximately $362 kg$ $StartFraction 330 Over 7 EndFraction$ days after it was born.

The predicted body mass of the animal was approximately $StartFraction 330 Over 7 EndFraction kg$ $362$ days after it was born.

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Explanation

Choice B is correct. In the statement " $m left parenthesis 330 right parenthesis$ is approximately equal to $362$ ," the input of the function, $330$ , is the value of $t$ , the elapsed time, in days, since the animal was born. The approximate value of the function, $362$ , is the predicted body mass, in kilograms, of the animal after that time has elapsed. Therefore, the predicted body mass of the animal was approximately $362 kg$ $330$ days after it was born.

Choice A is incorrect. This would be the best interpretation of the statement " $m left parenthesis 362 right parenthesis$ is approximately equal to $330$ ."

Choice C is incorrect. The number $StartFraction 330 Over 7 EndFraction$ is the number of weeks, not the number of days, after the animal was born.

Choice D is incorrect. This would be the best interpretation of the statement " $m left parenthesis 362 right parenthesis$ is approximately equal to $StartFraction 330 Over 7 EndFraction$ ."