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Chapter 12: Q42P (page 510)

Consider the exponential function e-x. Evaluate this function for x = 1, 10,000, and 0.01.

Short Answer

Expert verified

The value of exponent function for x=1,10,000is 0 and the value of exponent function for x=0.01 is 0.99.

Step by step solution

01

Identification of given data

The given data can be listed below,

  • values of the function are, x=1,10,000and0.01.
02

Concept/Significance of exponential function

The exponential and logarithmic functions are diametrically opposed. The exponential function is reversed by the logarithmic function.

03

Determination of values for function x

The function can be written as,

y=e-xIny=Ine-x

…(i)

Substitute first value of x in the above.

Iny=Ine-110000=1100002.3030logy=-110000logy=-47763.8y=10-47763.8=0

Thus, the value of exponent function for x=1,10,000is 0.

Substitute second value of x in equation (i),

Iny=Ine-0.01=-0.012.303logy=-0.01logy=-0.004342y=10-0.004342=0.99

Thus, the value of exponent function for x=0.01is 0.99.

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