Question

4 Find a formula for the exponential function passing through the points (-2, 4/9) and (3, 108)​

Answer 1

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Answer:

  f(x) = 4·3^x

Step-by-step explanation:

We assume the function will be of the form ...

  f(x) = a·b^x

Substituting the given values, we can find 'a' and 'b'.

  4/9 = a·b^(-2)

  108 = a·b^3

Dividing the second equation by the first gives ...

  108/(4/9) = b^(3 -(-2))

  243 = b^5

  b = 3 . . . . . . 5th root

Using the second equation, we can find 'a':

  108 = a·3^3 = 27a

  a = 108/27 = 4

The formula for the exponential function is ...

  f(x) = 4·3^x