Math / Algebra

QuestionEvaluate the function. Round answers to four decimal places, if necessary. $\begin{array}{l} f(x)=4(5)^{x}, \text { for } f(-3) . \\ f(-3)= \end{array}$ $\square$

Studdy Solution

STEP 1

1. We are given the function $f(x) = 4(5)^x$ .
2. We need to evaluate the function at $x = -3$ .
3. The answer should be rounded to four decimal places if necessary.

STEP 2

1. Substitute $x = -3$ into the function $f(x)$ .
2. Simplify the expression to find $f(-3)$ .
3. Round the result to four decimal places, if necessary.

STEP 3

Substitute $x = -3$ into the function:
$f(-3) = 4(5)^{-3}$

STEP 4

Simplify the expression:
$f(-3) = 4 \times \frac{1}{5^3}$ $f(-3) = 4 \times \frac{1}{125}$ $f(-3) = \frac{4}{125}$

STEP 5

Convert the fraction to a decimal and round to four decimal places:
$f(-3) = 0.032$
Since the decimal is already to four decimal places, no further rounding is necessary.
The value of $f(-3)$ is:
$\boxed{0.032}$

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QuestionEvaluate the function. Round answers to four decimal places, if necessary. $\begin{array}{l} f(x)=4(5)^{x}, \text { for } f(-3) . \\ f(-3)= \end{array}$ $\square$

Studdy Solution

STEP 1

1. We are given the function $f(x) = 4(5)^x$ .
2. We need to evaluate the function at $x = -3$ .
3. The answer should be rounded to four decimal places if necessary.

STEP 2

1. Substitute $x = -3$ into the function $f(x)$ .
2. Simplify the expression to find $f(-3)$ .
3. Round the result to four decimal places, if necessary.

STEP 3

Substitute $x = -3$ into the function:
$f(-3) = 4(5)^{-3}$

STEP 4

Simplify the expression:
$f(-3) = 4 \times \frac{1}{5^3}$ $f(-3) = 4 \times \frac{1}{125}$ $f(-3) = \frac{4}{125}$

STEP 5

Convert the fraction to a decimal and round to four decimal places:
$f(-3) = 0.032$
Since the decimal is already to four decimal places, no further rounding is necessary.
The value of $f(-3)$ is:
$\boxed{0.032}$

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QuestionEvaluate the function. Round answers to four decimal places, if necessary. f(x)=4(5)x, for f(−3).f(−3)=\begin{array}{l} f(x)=4(5)^{x}, \text { for } f(-3) . \\ f(-3)= \end{array}f(x)=4(5)x, for f(−3).f(−3)=​ □\square□

Studdy Solution

STEP 1

1. We are given the function f(x)=4(5)x f(x) = 4(5)^x f(x)=4(5)x.2. We need to evaluate the function at x=−3 x = -3 x=−3.3. The answer should be rounded to four decimal places if necessary.

STEP 2

1. Substitute x=−3 x = -3 x=−3 into the function f(x) f(x) f(x).2. Simplify the expression to find f(−3) f(-3) f(−3).3. Round the result to four decimal places, if necessary.

STEP 3

Substitute x=−3 x = -3 x=−3 into the function:f(−3)=4(5)−3 f(-3) = 4(5)^{-3} f(−3)=4(5)−3

STEP 4

Simplify the expression:f(−3)=4×153 f(-3) = 4 \times \frac{1}{5^3} f(−3)=4×531​ f(−3)=4×1125 f(-3) = 4 \times \frac{1}{125} f(−3)=4×1251​ f(−3)=4125 f(-3) = \frac{4}{125} f(−3)=1254​

STEP 5

Convert the fraction to a decimal and round to four decimal places:f(−3)=0.032 f(-3) = 0.032 f(−3)=0.032Since the decimal is already to four decimal places, no further rounding is necessary. The value of f(−3) f(-3) f(−3) is:0.032 \boxed{0.032} 0.032​

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QuestionEvaluate the function. Round answers to four decimal places, if necessary. $\begin{array}{l} f(x)=4(5)^{x}, \text { for } f(-3) . \\ f(-3)= \end{array}$ $\square$

1. We are given the function $f(x) = 4(5)^x$ .
2. We need to evaluate the function at $x = -3$ .
3. The answer should be rounded to four decimal places if necessary.

1. Substitute $x = -3$ into the function $f(x)$ .
2. Simplify the expression to find $f(-3)$ .
3. Round the result to four decimal places, if necessary.

Substitute $x = -3$ into the function:
$f(-3) = 4(5)^{-3}$

Simplify the expression:
$f(-3) = 4 \times \frac{1}{5^3}$ $f(-3) = 4 \times \frac{1}{125}$ $f(-3) = \frac{4}{125}$

Convert the fraction to a decimal and round to four decimal places:
$f(-3) = 0.032$
Since the decimal is already to four decimal places, no further rounding is necessary.
The value of $f(-3)$ is:
$\boxed{0.032}$