The growth of a certain type of weed satisfies a differential equation of the following form, where a is the height of the weed at maturity: dy = ky (a - y) dt Thus we know that the height, y(t), of the weed after t days have passed is given by the following equation: a y(t) = 1+ Be-akt If a typical weed has height 10 centimeters after 7 days, height 50 centimeters after 22 days, and reaches height 54 centimeters at maturity, find the values of the constants B and k (correct to at least 4 decimal places). B = k =

The growth of a certain type of weed satisfies a differential equation of the following form, where a is the height of the weed at maturity: dy = ky (a - y) dt Thus we know that the height, y(t), of the weed after t days have passed is given by the following equation: a y(t) = 1+ Be-akt If a typical weed has height 10 centimeters after 7 days, height 50 centimeters after 22 days, and reaches height 54 centimeters at maturity, find the values of the constants B and k (correct to at least 4 decimal places). B = k =

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

The growth of a certain type of weed satisfies a differential equation of the following form, where a is the height of the weed at maturity:
dy
= ky (a – y)
dt
Thus we know that the height, y(t), of the weed after t days have passed is given by the following equation:
a
y(t) =
1+ Be-akt
If a typical weed has height 10 centimeters after 7 days, height 50 centimeters after 22 days, and reaches height 54 centimeters at maturity, find the values of the constants B and k
(correct to at least 4 decimal places).
B =
k =

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