0. Functions

Exponential Functions

0. Functions

Exponential Functions

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Multiple Choice

Determine if the function is an exponential function.
If so, identify the power & base, then evaluate for $x=4$ .
$f\left(x\right)=\left(\frac12\right)^{x}$

Exponential function, $f\left(4\right)=\frac{1}{16}$

Exponential function, $f\left(4\right)=-16$

Not an exponential function

Verified step by step guidance

First, understand what an exponential function is. An exponential function is of the form $ f(x) = a^x $, where $ a $ is a constant base and $ x $ is the exponent.

Examine the given function $ f(x) = \left( \frac{1}{2} \right)^x $. This matches the form of an exponential function, where the base $ a $ is $ \frac{1}{2} $ and the exponent is $ x $.

Since the function is an exponential function, identify the base and the power. Here, the base is $ \frac{1}{2} $ and the power is $ x $.

To evaluate the function for $ x = 4 $, substitute $ x = 4 $ into the function: $ f(4) = \left( \frac{1}{2} \right)^4 $.

Calculate $ \left( \frac{1}{2} \right)^4 $ by multiplying $ \frac{1}{2} $ by itself four times: $ \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} $. This will give you the value of $ f(4) $.

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Related Practice

Multiple Choice

Given the following table of values for an exponential function $f (x)$ :

$x$	$f (x)$
$0$	$3$
$1$	$6$
$2$	$12$
$3$	$24$

What is the multiplicative rate of change of

f (x)

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Multiple Choice

Which operation can be used to eliminate the natural logarithm ( $\ln$ ) from both sides of an equation such as $\ln (x) = 3$ ?

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Multiple Choice

Determine if the function is an exponential function.

If so, identify the power & base, then evaluate for $x=4$ .

$f\left(x\right)=\left(-2\right)^{x}$

Determine if the function is an exponential function.

If so, identify the power & base, then evaluate for $x=4$ .

$f\left(x\right)=3\left(1.5\right)^{x}$

134

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Multiple Choice

Graph the given function.

$g\left(x\right)=e^{x+3}-1$

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Textbook Question

A culture of bacteria has a population of $150$ cells when it is first observed. The population doubles every $12~\text{hr}$ , which means its population is governed by the function $p\left(t\right)=150\cdot{2^{\frac{t}{12}}}$ , where $t$ is the number of hours after the first observation.