Integration

Rita Lamichhane

Student

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New University has an enrollment of 3000, but its projected rate of increase in number of students is dNdt=60000(t+1)−3/2. Find the projected number of students after t years. What is the projected number of students after 8 years?

  • 10 Feb, 2025
Replies (1)
Vidhyamath Guru

Instructor

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Solution:

N(t)=∫60000(t+1)−3/2 dt=60000×(−2(t+1)−1/2)+C=−120000(t+1)−1/2+C

Given N(0)=3000:

3000=−120000(1)−1/2+C⇒3000=−120000+C⇒C=123000

Thus, the formula is:

N(t)=−120000(t+1)−1/2+123000

For t=8:

N(8)=−120000(9)−1/2+123000=−120000×13+123000=−40000+123000=83000

  • 10 Feb, 2025

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