Chapter 6.4, Problem 54E

(a)

To determine

To find: Domain and range of the function.

Answer to Problem 54E

Both domain and range of the given function are all real numbers.

Explanation of Solution

Given information: $P=100{\left(0.99997\right)}^t$

The domain of the given function is all real numbers.

The range of the given function is all real numbers.

(b)

To determine

To find: The remaining plutonium $-239$ .

Answer to Problem 54E

The remaining plutonium $-239$ is $69.77$ .

Explanation of Solution

Given information: $P=100{\left(0.99997\right)}^t$ and $t=12000years$

Calculation: The remaining plutonium $-239$ after $t=12000years$ ,

  $\begin{array}{l}P=100{\left(0.99997\right)}^{12000}\\ P=100\times 0.697672\\ P\simeq 69.77\end{array}$

(c)

To determine

To describe: The transformation of the function..

Answer to Problem 54E

The function is vertically stretched by a factor of $5.5$ .

Explanation of Solution

Given information: $P=100{\left(0.99997\right)}^t$ and initial amount of plutonium were $550$ grams.

Calculation: Since initial amount of plutonium were $550$ grams.

  $\therefore P=550{\left(0.99997\right)}^t$

Find the factor by division, if $t=12000years$

  $\therefore \frac{P_{550}}{P_{100}}=\frac{500{\left(0.99997\right)}^{12000}}{100{\left(0.99997\right)}^{12000}}=5.5$

The function is vertically stretched by a factor of $5.5$ .

(d)

To determine

To explain: Whether the domain and range of the function changes when its transformation occur.

Answer to Problem 54E

No! There will be no change.

Explanation of Solution

Given information: From part (c) $P=550{\left(0.99997\right)}^t$

Calculation: Since domain and range of the function are for all real numbers. So any changes in the factor of function do not change the domain and range.