Determine if the function is an exponential function.
If so, identify the power & base, then evaluate for $x=4$ .
$f$\left$(x$\right$)=$\left$($\frac$12$\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) $.

6:13m

Watch next

Master Exponential Functions with a bite sized video explanation from Patrick

Related Videos

Related Practice

Textbook Question

23. Human evolution continues The analysis of tooth shrinkage by C. Loring Brace and colleagues at the University of Michigan’s Museum of Anthropology indicates that human tooth size is continuing to decrease and that the evolutionary process has not yet come to a halt. In northern Europeans, for example, tooth size reduction now has a rate of 1% per 1000 years.

a. If t represents time in years and y represents tooth size, use the condition that y=0.99y_0 when t=1000 to find the value of k in the equation y=y_0 e^(kt). Then use this value of k to answer the following questions.

views

Textbook Question

31. The incidence of a disease (Continuation of Example 4.) Suppose that in any given year the number of cases can be reduced by 25% instead of 20%.

b. How long will it take to eradicate the disease—that is, reduce the number of cases to less than 1?

views

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$)^{x}$

Graph the given function.

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

277

views

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.