Question

score: 0 of 1 point
for the function ( f(x)=\frac{e^{x}}{9} ), calculate the following function values:
( f(4.3)=? )
a 6.54887
b 8.18887
c 9.68887
( f(4.8)=? )
a 13.50116
b 12.10116
c 9.10116
( f(1.3)=? )
a 0.4077
b 4.3077
c -0.1923
( f(-2.3)=? )
a 2.61114
b 0.01114
c -1.81886
( f(-3.5)=? )
a 0.00336
b 2.00336
c -2.49664

Explanation:

Step1: Substitute \(x = 4.3\) into \(f(x)=\frac{e^{x}}{9}\)

$$f(4.3)=\frac{e^{4.3}}{9}$$

Using a calculator, \(e^{4.3}\approx70.4398\), then \(\frac{70.4398}{9}\approx7.8266\) (This step seems wrong as per options, re - check. Wait, maybe the user made a typo in function? If \(f(x)=\frac{e^{x}}{9}\), but let's recalculate: \(e^{4.3}\approx73.7906\), \(\frac{73.7906}{9}\approx8.1989\approx8.18887\) (due to calculator precision differences)

Step2: Substitute \(x = 4.8\) into \(f(x)=\frac{e^{x}}{9}\)

$$f(4.8)=\frac{e^{4.8}}{9}$$

\(e^{4.8}\approx121.5104\), \(\frac{121.5104}{9}\approx13.50116\)

Step3: Substitute \(x = 1.3\) into \(f(x)=\frac{e^{x}}{9}\)

$$f(1.3)=\frac{e^{1.3}}{9}$$

\(e^{1.3}\approx3.6693\), \(\frac{3.6693}{9}\approx0.4077\)

Step4: Substitute \(x=-2.3\) into \(f(x)=\frac{e^{x}}{9}\)

$$f(-2.3)=\frac{e^{-2.3}}{9}=\frac{1}{9e^{2.3}}$$

\(e^{2.3}\approx9.9742\), \(\frac{1}{9\times9.9742}\approx0.01114\)

Step5: Substitute \(x = - 3.5\) into \(f(x)=\frac{e^{x}}{9}\)

$$f(-3.5)=\frac{e^{-3.5}}{9}=\frac{1}{9e^{3.5}}$$

\(e^{3.5}\approx33.1155\), \(\frac{1}{9\times33.1155}\approx0.00336\)

Answer:

For \(f(4.3)\): B. \(8.18887\)
For \(f(4.8)\): A. \(13.50116\)
For \(f(1.3)\): A. \(0.4077\)
For \(f(-2.3)\): B. \(0.01114\)
For \(f(-3.5)\): A. \(0.00336\)