Question

Ab? that goes through points (0,2)

Answer 1

Answer:

  y = 2·5^x

Step-by-step explanation:

Using the given points, we can solve for 'a' and 'b'.

  y = ab^x

  2 = ab^0 = a . . . . . substitute (0, 2) for (x, y)

__

  1250 = 2·b^4 . . . . substitute for 'a' and (4, 1250) for (x, y)

  625 = b^4 . . . . divide by 2

  5 = b . . . . . . . take the 4th root

The function is ...

  y = 2·5^x

____

Additional comment

There are two real and two imaginary 4th roots of 625. Only the positive real root is useful as the base in an exponential function like this.