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¬4³. (a) Calculate the rate of growth, dL/dt, at t =15, 20, and 30 weeks (you can use a calculator to give a decimal approximation). Does the rate of growth of the fetus increase or decrease as it ages? (b) Write a sentence interpreting L'(15) value in terms of the femur length, including units.
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¬4³. (a) Calculate the rate of growth, dL/dt, at t =15, 20, and 30 weeks (you can use a calculator to give a decimal approximation). Does the rate of growth of the fetus increase or decrease as it ages? (b) Write a sentence interpreting L'(15) value in terms of the femur length, including units.
Chapter6: Exponential And Logarithmic Functions
Section6.8: Fitting Exponential Models To Data
Problem 3TI: Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to...
Related questions
Question
Transcribed Image Text:Question 6 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 × 10¬4³.
(a) Calculate the rate of growth, dL/dt, at t =15, 20, and 30 weeks (you can use a calculator to give
a decimal approximation). Does the rate of growth of the fetus increase or decrease as it ages?
(b) Write a sentence interpreting L'(15) value in terms of the femur length, including units.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage