Question

A population is modeled by the differential equation $dx/dt = x^2 - 12 + 32$, where time is expressed in years. What are the population's critical points? For each critical point, show that it is stable or unstable. If the initial population is 2, what is the population 0.15 years later? Round your answer to the nearest integer.

Name: A population is modeled by the differential equation dx/dt = x^2 - 12 + 32, where time is expressed in years. What are the population's critical points? For each critical point, show that it is stable or unstable. If the initial population is 2, what is the population 0.15 years later? Round your answer to the nearest integer.
Uploaded: 2022-03-15T21:45:56-08:00
Duration: 4 min 49 s
Channel: Shannon K
Description: A population is modeled by the differential equation dx/dt = x^2 - 12 + 32, where time is expressed in years. What are the population's critical points? For each critical point, show that it is stable or unstable. If the initial population is 2, what is the population 0.15 years later? Round your answer to the nearest integer.

          A population is modeled by the differential equation $dx/dt = x^2 - 12 + 32$, where time is expressed in years. What are the population's critical points? For each critical point, show that it is stable or unstable. If the initial population is 2, what is the population 0.15 years later? Round your answer to the nearest integer.

A population is modeled by the differential equation dx/dt = x^2 - 12 + 32, where time is expressed in years. What are the population's critical points? For each critical point, show that it is stable or unstable. If the initial population is 2, what is the population 0.15 years later? Round your answer to the nearest integer.

Added by David F.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Shannon K

03/15/2022

Step 1

Given: dx/dt = x^2 - 12 + 32 Setting dx/dt = 0, we have: 0 = x^2 - 12 + 32 x^2 = 12 - 32 x^2 = -20 x = ±√(-20) x = ±2√5 Therefore, the critical points are x = 2√5 and x = -2√5. Show more…

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A population is modeled by the differential equation d(x)/(d)t=x^(2)-12+32, where time is expressed in years. What are the population's critical points? For each critical point, show that it is stable or unstable. If the initial population is 2 , what is the population 0.15 years later? Round your answer to the nearest integer. A population is modeled by the differential equation dx/dt = x2 -12 + 32, where time is expressed in years. What are the population's critical points? For each critical point,show that it is stable or unstable.If the initial population is 2,what is the population 0.15 years later? Round your answer to the nearest integer.