For children between the ages of 5 and 13 years, the Ehrenberg equationln W = ln 2.4 + 1.84hgives the relationship between the weight W (in kilograms) and the height h (in meters) of a child. Use differentials to estimate the change in the weight of a child who grows from 1.4 m to 1.5 m. (Round your answer to two decimal places.)

Question
Asked Oct 25, 2019

For children between the ages of 5 and 13 years, the Ehrenberg equation

ln W = ln 2.4 + 1.84h

gives the relationship between the weight W (in kilograms) and the height h (in meters) of a child. Use differentials to estimate the change in the weight of a child who grows from 1.4 m to 1.5 m. (Round your answer to two decimal places.)

check_circleExpert Solution
Step 1

Given data;

n W n 2.41.84h
.....(1)
for h=1.4
In W In 2.4+1.84 (1.4)
n W-n 2.4 = 2.576
W
In
2.576
2.4
= e2576
2.4
W 2.4e2576(2.4) (13.1444) 31.546
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n W n 2.41.84h .....(1) for h=1.4 In W In 2.4+1.84 (1.4) n W-n 2.4 = 2.576 W In 2.576 2.4 = e2576 2.4 W 2.4e2576(2.4) (13.1444) 31.546

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Step 2

Differentiate equation ...

In W
In 2.41.84h
1
-dW 0+1.84dh
W
dW (W) (1.84dh)
...(2)
Since the height changes from 1.4m to 1.5m, dh-0.1
Substitute value for W from Step 1 and dh = 0.1 in Equati on (2)
dW (31.546) (1.84 [0.1])
dW (31.546) (0.184)
dW 5.80
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In W In 2.41.84h 1 -dW 0+1.84dh W dW (W) (1.84dh) ...(2) Since the height changes from 1.4m to 1.5m, dh-0.1 Substitute value for W from Step 1 and dh = 0.1 in Equati on (2) dW (31.546) (1.84 [0.1]) dW (31.546) (0.184) dW 5.80

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Tagged in

Math

Calculus

Derivative