Chapter 4, Problem 1CC

To determine

(a)

To write:

The exponential function $f$ with the base as $a$.

Answer to Problem 1CC

The exponential function $f$ with base $a$ is $f\left(x\right)=a^x$.

Explanation of Solution

Given information:

The exponential function $f$ with base $a$.

Calculation:

The exponential function $f$ can be written for any real number $x$ with base $b$ as,

$f\left(x\right)=b^x$ ...... (1)

Here, $b>0$ and $b\ne 0$.

Substitute a for b to obtain an exponential function $f$ for any real number $x$ with base $a$ as,

$f\left(x\right)=a^x$

Conclusion:

Thus, the exponential function $f$ with base $a$ is $f\left(x\right)=a^x$.

To determine

(b)

To write:

The exponential function $f$ with base is given as $3$.

Answer to Problem 1CC

The exponential function $f$ with base $3$ is $f\left(x\right)=3^x$.

Explanation of Solution

Given information:

The exponential function $f$ with base $3$.

Calculation:

From part (a), the formula for exponential function for any real number $x$ with base $a$ is

$f\left(x\right)=a^x$ ...... (2)

Substitute 3 for a to obtain the exponential function $f$ for any real number $x$ with base $3$ as,

$f\left(x\right)=3^x$

Conclusion:

Thus, the exponential function $f$ with base $3$ is $f\left(x\right)=3^x$.