The functions f, g, h, and k are,[tex]y = 15 .( 3) ^x[/tex] , [tex]y = 26 .( 0.5) ^x[/tex] , [tex]y = 7 .( 8) ^x[/tex] and, [tex]y = 280 .( 0.143) ^x[/tex] respectively.
How to model monotonous functions?
A function is monotonous when is either increasing or decreasing for all values of x.
A power function is a case of a monotonous function, whose model is defined;
[tex]y = y_0 .r ^x[/tex]
Where:
y_0 - Initial value
r - Increase rate
x - Independent variable
y - Dependent variable
Case 1 (f(x) - Initial value: 5, increase rate: 3)
[tex]y = 15 .( 3) ^x[/tex] (2)
Case 2 (g(x) - Initial value: 26, increase rate: 0.5)
[tex]y = 26 .( 0.5) ^x[/tex] (3)
Case 3 (h(x) - Initial value: 7, increase rate: 8)
[tex]y = 7 .( 8) ^x[/tex] (4)
Case 4 (k(x) - Initial value: 280, increase rate: 0.143)
[tex]y = 280 .( 0.143) ^x[/tex] (5)
Hence, The functions f, g, h, and k are,[tex]y = 15 .( 3) ^x[/tex] , [tex]y = 26 .( 0.5) ^x[/tex] , [tex]y = 7 .( 8) ^x[/tex] and, [tex]y = 280 .( 0.143) ^x[/tex] respectively.
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