Question

3. A new species of fish is introduced into a lake. The initial population is 200, and it increases by 10% each month. (Hint. Note that $a + ar + \dots + ar^n = \frac{a(1 - r^{n+1})}{1 - r}$) • (a) (1 mark) Write a sequence that represents the fish population at the end of each month for the next 24 months. • (b) (1 mark) Find the sum of the series representing the total fish population over the 24-month period. • (c) (1 mark) Discuss the long-term behavior of the fish population if this growth rate continues indefinitely.

          3. A new species of fish is introduced into a lake. The initial population is 200, and it increases by 10% each month.
(Hint. Note that $a + ar + \dots + ar^n = \frac{a(1 - r^{n+1})}{1 - r}$)
• (a) (1 mark) Write a sequence that represents the fish population at the end of each month for the next 24 months.
• (b) (1 mark) Find the sum of the series representing the total fish population over the 24-month period.
• (c) (1 mark) Discuss the long-term behavior of the fish population if this growth rate continues indefinitely.

3. A new species of fish is introduced into a lake. The initial population is 200, and it increases by 10% each month.
(Hint. Note that a + ar + … + ar^n = (a(1 - r^n+1))/(1 - r))
• (a) (1 mark) Write a sequence that represents the fish population at the end of each month for the next 24 months.
• (b) (1 mark) Find the sum of the series representing the total fish population over the 24-month period.
• (c) (1 mark) Discuss the long-term behavior of the fish population if this growth rate continues indefinitely.

Added by Jonathan F.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Naresh Bagrecha

12/22/2021

Step 1

This means that the population is multiplied by 1.1 each month. Show more…

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3. A new species of fish is introduced into a lake. The initial population is 200, and it increases by 10% each month. (Hint. Note that a + ar + ... + arn = $$ \frac{a(1-r^{n+1})}{1-r} $$. ) • (a) (1 mark) Write a sequence that represents the fish population at the end of each month for the next 24 months. • (b) (1 mark) Find the sum of the series representing the total fish population over the 24-month period. • (c) (1 mark) Discuss the long-term behavior of the fish population if this growth rate continues indefinitely.