Convert the exponential function to the form indicated. (Round all coefficients to four significant digits.)
Given: [tex]f(x) = 2.5 e^{-0.7x}[/tex]
Convert to: [tex]f(x) = A b^x[/tex]
Find:
- [tex]A = ?[/tex]
- [tex]b = ?[/tex]
Answer (2)
f ( x ) = 2.5 e − 0.7 x = 2.5 ( e − 0.7 ) x A = 2.5 b = e − 0.7
The exponential function f ( x ) = 2.5 e − 0.7 x can be converted to the form f ( x ) = A b x where A = 2.500 and b ≈ 0.4966 . Thus, the final form is f ( x ) = 2.500 ( 0.4966 ) x .
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