Question

Ultrasound is often used to make images of developing fetuses. In particular, by measuring the size of a fetus ultrasound technicians can estimate its age and then predict its birthdate. To do this requires formulas for fetus size as a function of age. Verbung et al. (2008) fit data from over 6000 fetal ultrasounds. They measured the femur length, L, (in mm) as a function of the fetus age, t, (in weeks) and found the following formula

L= -37.50 + 3.71t- 6.33 x 10^-4t^3.

Required:
a. Calculate the rate of growth, dL/dt, at t =15, 20, and 30 weeks.
b. Write a sentence interpreting L'(15) value in terms of the femur length.

Answer 1

The rate of fetal femur growth, dL/dt, is calculated at different week intervals and the L'(15) value indicates an approximate femur length growth rate of 3.58 mm per week at 15 weeks of age.

Step-by-step explanation:

To calculate the rate of growth of the fetal femur length with respect to time, dL/dt, we need to take the derivative of the given formula L = -37.50 + 3.71t - 6.33 x 10-4t3 with respect to t. The derivative, which represents the rate of growth of the femur length, is dL/dt = 3.71 - 3 * 6.33 x 10-4t2.

At t = 15 weeks, the rate of growth is dL/dt = 3.71 - 3 * 6.33 x 10-4 * 152, which simplifies to a rate of approximately 3.58 mm/week.

At t = 20 weeks, the rate of growth is dL/dt = 3.71 - 3 * 6.33 x 10-4 * 202, which simplifies to a rate of approximately 3.29 mm/week.

At t = 30 weeks, the rate of growth is dL/dt = 3.71 - 3 * 6.33 x 10-4 * 302, which simplifies to a rate of approximately 2.19 mm/week.

To interpret the value L'(15), we say that at 15 weeks of age, the femur length of a fetus is increasing at a rate of approximately 3.58 mm per week.

Answer 2

Answer:Fetal growth The growth of a fetus more than 12 weeks old can be approximated by the formula L=1.53t−6.7, where L is the length (in centimeters) and t is the age (in weeks). Prenatal length can be determined by ultrasound. Approximate the age of a fetus whose length is 28 centimeters.

Explanation:hope this helps