Chapter 8.2, Problem 46HP

(a)

To determine

To find: whether the statement is sometimes, always or never true.

Answer to Problem 46HP

The statement $2^x>-8^{20x}$ is true for all values of $x$ .

Explanation of Solution

Given information:

The statement $2^x>-8^{20x}$ for all values of $x$ .

Consider the given statement $2^x>-8^{20x}$ . $2^x>-8^{20x}$ are positive for all values of $x$ . It is clear from the given statement that $-8^{20x}<0$ for all values of $x$ . Now multiply the inequality $-8^{20x}<0$ by $-1$ . So, the reverse of the inequality. It implies,

(b)

To determine

To find: Whether the statement is sometimes, always or never true.

Answer to Problem 46HP

The Statement is sometime true.

Explanation of Solution

Given information:The given statement is “the graph of exponential growth function is increasing”.

Consider the general exponential function.

  $y=a^x$

Since, the all exponential function increases for all the interval $\left(0,\infty \right)$ otherwise function will decrease.

So, the statement is sometime true.

Therefore, the Statement is sometime true.

(c)

To determine

To find: Whether the statement is sometimes, always or never true.

Answer to Problem 46HP

Explanation of Solution

Given information:

The given statement is “the graph of exponential decay function is increasing”.

Consider the general exponential function.

  $y=a^{-x}$

Since, the all exponential decay function increases for all the interval $\left(-\infty ,0\right)$ otherwise function will decrease.

So, the statement is sometime true.

Therefore, the Statement is sometime true.