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? AP = k(100 – V) AP = 100 – kV %3D dt dt
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? AP = k(100 – V) AP = 100 – kV %3D dt dt
Chapter5: Exponential And Logarithmic Functions
Section5.5: Exponential And Logarithmic Models
Problem 30E: The table shows the mid-year populations (in millions) of five countries in 2015 and the projected...
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Will k be positive or negative? Why?
Transcribed Image Text: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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