### Solution Found!

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

**Chapter 2, Problem 60A**

(choose chapter or problem)

**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.