Math  /  Differential Equations

Question Fetal head circumference HH depends on age tt in weeks as H=30.04+1.802t20.9032t2logtH=-30.04+1.802t^2-0.9032t^2\log t. (a) Calculate dHdt\frac{dH}{dt}. (b) Is dHdt\frac{dH}{dt} larger at t=8t=8 or t=36t=36 weeks? (c) Repeat (b) for 1HdHdt\frac{1}{H}\frac{dH}{dt}. (a) dHdt=3.604t0.9032tlogt0.9032t\frac{dH}{dt}=3.604t-0.9032t\log t-0.9032t.

Studdy Solution
Compare the values obtained in STEPS 21 and 25 to determine when the fractional rate of growth is larger.
(c) The fractional rate of growth 1HdHdt \frac{1}{H} \frac{dH}{dt} is larger at the age which gives the higher numerical value from the calculations in STEPS 21 and 25.
The actual numerical calculations for dHdt \frac{dH}{dt} at t=8 t = 8 and t=36 t = 36 weeks, as well as the values of H H at these times, and the fractional rates of growth, would require a calculator or computational tool to complete. The steps provided outline the process to obtain these values.

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