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svetoff [14.1K]
3 years ago
13

A type of plant is introduced into an ecosystem and quickly begins to take over. A scientist counts the number of plants after m

months and develops the equation P(m) = 19.3(1.089)^m to model the situation. Most recently, the scientist counted 138 plants. Assuming there are no limiting factors to the growth of the plants, about how many months have passed since the plants were first introduced?
6.1
6.6
7.2
23.1
Mathematics
1 answer:
mr_godi [17]3 years ago
4 0

Answer:

D. 23.1

Step-by-step explanation:

Late answer

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18 = r^2 + 3r

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Now, differentiating equation (1) with respect to t ( time ),

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∵ h = constant, ⇒ dh/dt = 0,

\frac{dA}{dt} = 4\pi r \frac{dr}{dt} +2\pi h \frac{dr}{dt}

We have, \frac{dA}{dt}=9\pi\text{ square meters per hour}, r = h = 3\text{ meters}

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9\pi = (12\pi + 6\pi )\frac{dr}{dt}

9\pi = 18\pi \frac{dr}{dt}

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Now,

Volume of a cylinder,

V=\pi r^2 h

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\frac{dV}{dt}=\pi ( r^2 \frac{dh}{dt}+h(2r)\frac{dr}{dt})=\pi ((3)(6) (\frac{1}{2})) = 9\pi \text{ cubic meters per hour}

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