Chapter 3.1, Problem 59E

Solution

To decide: if the given statement is true or false.

False

Given information:

The statement, “Every exponential function is strictly increasing.”

Definition Used:

Exponential Growth and Decay:

For an exponential function $f\left(x\right)=a\cdot b^x$ and any real number x ,

  $f\left(x+1\right)=b\cdot f\left(x\right)$

If $a>0$ and $b>1$, the function f is increasing and is an exponential growth function. The base b is its growth factor.

If $a>0$ and $0<b<1$, the function f is decreasing and is an exponential decay function. The base b is its decay factor.

Explanation:

It follows from the above definition that an exponential function can be both increasing and decreasing and it depends on the value of the base ‘ b’ .

For example, consider the exponential function $f\left(x\right)={0.5}^x$

As for this function base is $b=0.5$ which satisfies $0<b<1$, so by using the above definition this function is an exponential decay function and hence is decreasing.

Thus, the given statement is false.