Question

Write a exponential function

Answer 1

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Answer 2

`y = 0.0625(2) {}^(x)`

Step by step

`y = a(b^(x) )`

X = 1 y = 0.125

`0.125 = ab^(1) \\ a = (0.125)/(b)`

X = 4 y = 1

`1 = a( {b}^(4) ) \\ ab^(4) = 1 \\ replace \: a = (0.125)/(b) \: in \: ab^(4) = 1 \\ (0.125)/(b) * b^(4) = 1 \\ {b}^(3) = (1)/(0.125) \\ b = \sqrt[3]{ (1)/(0.125) } \\ b = 2`

`replace \: b = 2 \: in \: a = (0.125)/(b) \\ a = (0.125)/(2) \\ a = 0.0625`

`therefore \: \\ y = 0.0625( {2})^(x)`