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Tooth Length The length (in mm) of the mesiodistal crown

Chapter 2, Problem 60A

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QUESTION:

Problem 60A

Tooth Length The length (in mm) of the mesiodistal crown of the first molar for human fetuses can be approximated by

L(t) = −0.01t2 + 0.788t − 7.048,

where t is the number of weeks since conception. Source: American Journal of Physical Anthropology.

a. What does this formula predict for the length at 14 weeks? 24 weeks?

b. What does this formula predict for the maximum length, and when does that occur? Explain why the formula does not make sense past that time.

Questions & Answers

QUESTION:

Problem 60A

Tooth Length The length (in mm) of the mesiodistal crown of the first molar for human fetuses can be approximated by

L(t) = −0.01t2 + 0.788t − 7.048,

where t is the number of weeks since conception. Source: American Journal of Physical Anthropology.

a. What does this formula predict for the length at 14 weeks? 24 weeks?

b. What does this formula predict for the maximum length, and when does that occur? Explain why the formula does not make sense past that time.

ANSWER:

Solution

Step 1 of 3

In this problem, we have given that the length (in mm) of the mesiodistal crown of the first molar for human fetuses can be approximated by

 where  is the number of weeks

(a). Here we have to find the length at  weeks and  weeks

For , we get

Hence the length at  weeks is  mm.

For , we get

Hence the length at  weeks is  mm.


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