The logistic growth model describing the changing height of a sunflower, H, in cm. as a function of time, t, in days, can be written as dH = 0.004H (260 - H)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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FROM THE GIVEN INFORMATION, 

The logistic growth model describing the changing height of a sunflower, H, in cm. as a function of time, t,
in days, can be written as
dH
dt
= 0.004H (260- H)
Transcribed Image Text:The logistic growth model describing the changing height of a sunflower, H, in cm. as a function of time, t, in days, can be written as dH dt = 0.004H (260- H)
The condition is, H (7) = 17.9;
260
1+ Ce-0.004 (7)
17.9=
⇒1+C₂-0.004(7)
⇒C₂ -0.004(7)
⇒
-662) = 5-
260
17.9
260
17.9'
¡-1)×
⇒C 13.9092;
⇒H(t)=
- 1;
0.004x(7).
xeº
260
1+13.9092xe-0.004z
Transcribed Image Text:The condition is, H (7) = 17.9; 260 1+ Ce-0.004 (7) 17.9= ⇒1+C₂-0.004(7) ⇒C₂ -0.004(7) ⇒ -662) = 5- 260 17.9 260 17.9' ¡-1)× ⇒C 13.9092; ⇒H(t)= - 1; 0.004x(7). xeº 260 1+13.9092xe-0.004z
Expert Solution
Step 1

We will use given logistic growth model and integrate it to find value of H(t) . 

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