question\nif $f(x)=-2e^{x}$, find $f(-2)$.\nround your answer to the nearest hundredth, and if necessary…

question\nif $f(x)=-2e^{x}$, find $f(-2)$.\nround your answer to the nearest hundredth, and if necessary, include a leading 0 with any decimals less than 1. for example, 0.5 instead of .5.\nprovide your answer below:

question\nif $f(x)=-2e^{x}$, find $f(-2)$.\nround your answer to the nearest hundredth, and if necessary, include a leading 0 with any decimals less than 1. for example, 0.5 instead of .5.\nprovide your answer below:

Answer

Explanation:

Step1: Substitute x = -2

Substitute $x=-2$ into $f(x)=-2e^{x}$, we get $f(-2)=-2e^{-2}$.

Step2: Evaluate the exponential

Since $e^{-2}=\frac{1}{e^{2}}$, and $e\approx2.71828$, then $e^{2}\approx(2.71828)^{2}=7.389056$. So $e^{-2}=\frac{1}{7.389056}\approx0.135335$.

Step3: Calculate f(-2)

$f(-2)=-2\times0.135335=-0.27067$.

Step4: Round to nearest hundredth

Rounding $-0.27067$ to the nearest hundredth gives $-0.27$.

Answer:

$-0.27$