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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 1, Problem 27RE

(a)

To determine

**To find:** The quantity of mass that remains after 16days.

Expert Solution

**Solution:**

The quantity of mass that remains after 16days is

**Given:**

The initial mass of the sample = 1g.

The half-life of Palladium-100

**Calculation:**

Let the mass be *m*.

The initial mass = *m* and the mass of Palladium-100 in 4days =

The mass after 8days=

The mass after 12days=

The mass after 16days=

Since the initial mass *m* = 1*g*, the quantity of mass after 16 days is,

Thus, the mass that remains after 16days is

(b)

To determine

**To find:** The mass that remains after *t* days.

Expert Solution

**Solution:**

The mass that remains after *t* days is

**Given:**

The initial mass of the sample=1*g*.

The half-life of Palladium-100

**Calculation:**

From part (a), the mass after 16 days is,

The general form of the mass after *n* days is given by,

Therefore, the mass remains after *t* days is

(c)

To determine

**To find:** The inverse of

Expert Solution

**Solution:**

The inverse of the function is *m* gram is left.

**Laws of logarithms:**

If *x* and *y* are positive numbers, then

**Calculation:**

Let *t* days.

Then its inverse function is,

Here,

Taking

Simplify further as,

Substitute *t* value in the equation (2)

Thus,

Therefore, the inverse of the function is *m* grams left.

(d)

To determine

**To find:** When the mass is reduced to 0.01g.

Expert Solution

**Solution:**

The mass is reduced to 0.01g approximately in 26.6 days.

**Calculation:**

From part (a),

Substitute

Taking

On further simplification,

Therefore, the mass is reduced to 0.01g approximately in 26.6 days.