Find the correct differential equation and use separation of variables to solve the differential equation you chose. Use the values given to solve to find the two constants. 2. A climbing vine is taking over the side of a building. At first the vine only covered 10% of the building, butafter 4 years it covered 48%.The vine grows at a rate proportional to the percentage of the building that is not covered. Let V be thepercentage of the building covered with the vine (so V(0) = 10), and let t be time in years.%3D(a) Which differential equation correctly models this situation? Why?dVdV= k(100 – V)dt100 kVdt%3D|3D

18%. e proportional to the percentage of the building that is not covered. LetV be the ng covered with the vine (so V (0) = 10), and let t be time in years. %3D equation correctly models this situation? Why?

18%. e proportional to the percentage of the building that is not covered. LetV be the ng covered with the vine (so V (0) = 10), and let t be time in years. %3D equation correctly models this situation? Why?

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter2: Exponential, Logarithmic, And Trigonometric Functions

Section2.3: Applications: Growth And Decay

Problem 15E

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Question

Find the correct differential equation and use separation of variables to solve the differential equation you chose. Use the values given to solve to find the two constants.

2. A climbing vine is taking over the side of a building. At first the vine only covered 10% of the building, but
after 4 years it covered 48%.
The vine grows at a rate proportional to the percentage of the building that is not covered. Let V be the
percentage of the building covered with the vine (so V(0) = 10), and let t be time in years.
%3D
(a) Which differential equation correctly models this situation? Why?
dV
dV
= k(100 – V)
dt
100 kV
dt
%3D
|3D

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