Question

complete the table for the function ( y = 4e^{x} ). round each value to the nearest tenth.

( x )	( -1 )	( 0 )	( 1 )	( 2 )

Explanation:

Step1: Substitute \(x = - 1\)

Substitute \(x=-1\) into \(y = 4e^{x}\), we get \(y = 4e^{-1}=\frac{4}{e}\approx\frac{4}{2.718}\approx1.5\)

Step2: Substitute \(x = 0\)

Substitute \(x = 0\) into \(y = 4e^{x}\), we get \(y=4e^{0}=4\times1 = 4.0\)

Step3: Substitute \(x = 1\)

Substitute \(x = 1\) into \(y = 4e^{x}\), we get \(y = 4e^{1}\approx4\times2.718\approx10.9\)

Step4: Substitute \(x = 2\)

Substitute \(x = 2\) into \(y = 4e^{x}\), we get \(y = 4e^{2}\approx4\times7.389\approx29.6\)

Answer:

When \(x=-1\), \(y\approx1.5\); when \(x = 0\), \(y = 4.0\); when \(x=1\), \(y\approx10.9\); when \(x = 2\), \(y\approx29.6\)