Question

researchers fit data from over 6000 fetal ultrasounds. they measured the femur length, l, (in millimeters) as a function of the fetus age, t, (in weeks) and found the formula below. calculate the rate of growth, $\frac{d l}{d t}$, at t = 10, 15, and 25 weeks. does the rate of growth of the fetus increase or decrease as it ages?

l=-37.60 + 3.71t-6.32×10^{-4}t^{3}

write a function for $\frac{d l}{d t}$.

$\frac{d l}{d t}=3.71 - 0.001896t^{2}$

(use integers or decimals for any numbers in the expression.)

calculate the rate of growth at t = 10 weeks.

$\frac{d l}{d t}=\square mm/week$

(round to two decimal places as needed.)

Explanation:

Step1: Substitute \( t = 10 \) into \( \frac{dL}{dt}=3.71 - 0.001896t^{2} \)

$$
LATEXBLOCK0
$$

Step2: Calculate the value

$$ \frac{dL}{dt}=3.5204\approx3.52 $$

Answer:

\(3.52\)