Question

solve $-2^{x} = 0.5x$ by completing the table.
enter the outputs in the boxes. express any fractional values as decimals.

$x$	$f(x) = -2^{x}$	$g(x) = 0.5x$
$-1$	$square$	$square$
$0$	$square$
$1$	$square$
$2$	$square$

(there is a virtual keyboard image at the bottom, omitted here)

Explanation:

Step1: Calculate $f(-2)$

$f(-2) = -2^{-2} = -\frac{1}{2^2} = -0.25$

Step2: Calculate $g(-2)$

$g(-2) = 0.5(-2) = -1$

Step3: Calculate $f(-1)$

$f(-1) = -2^{-1} = -\frac{1}{2^1} = -0.5$

Step4: Calculate $g(-1)$

$g(-1) = 0.5(-1) = -0.5$

Step5: Calculate $f(0)$

$f(0) = -2^{0} = -1$

Step6: Calculate $g(0)$

$g(0) = 0.5(0) = 0$

Step7: Calculate $f(1)$

$f(1) = -2^{1} = -2$

Step8: Calculate $g(1)$

$g(1) = 0.5(1) = 0.5$

Step9: Calculate $f(2)$

$f(2) = -2^{2} = -4$

Step10: Calculate $g(2)$

$g(2) = 0.5(2) = 1$

Step11: Identify solution

Find $x$ where $f(x)=g(x)$

Answer:

Completed Table:

$x$	$f(x)=-2^x$	$g(x)=0.5x$
$-1$	$-0.5$	$-0.5$
$0$	$-1$	$0$
$1$	$-2$	$0.5$
$2$	$-4$	$1$

Solution to $-2^x=0.5x$:

$x=-1$