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6th Edition

Stewart + 5 others

Publisher: Cengage Learning

ISBN: 9780840068071

Chapter 1.5, Problem 115E

(a)

To determine

The date on which the fish population will be the same as it was on January 1, 2002.

Expert Solution

The fish population will be the same as it was on January 1, 2002 after

**Given:**

The fish population in a certain lake rises and falls according to the formula

**Calculation:**

Substitute

Therefore, the initial fish population is

Substitute

Simplify the above equation as follows.

So, the population of fish will be same again as it was on

Thus, the fish population will be the same as it was on January 1, 2002 after

(b)

To determine

The date by which all the fish in the lake will be dead.

Expert Solution

All the fish in the lake will be dead after

**Formula used:**

*Quadratic formula:*

The solution of a quadratic equation of the form

**Calculation:**

The number of fish will be zero when all the fish in the lake are dead.

Therefore, substitute

Use Quadratic formula to find the value of *t*.

Substitute

Simplify the above equation as follows.

The number of years must be positive.

Therefore, all the fish in lake will be dead after

Assuming that there will be 365 days in a year, convert 0.612 years to days.

That is, all the fish in lake will be dead after

By using a calendar, it is obtained that all the fish will be dead on

Thus, all the fish in the lake will be dead after