Question

Write an exponential function in the form y = ab” that goes through points (0,18)

and (3,9216).​

Answer 1

it's y=18*2^x

Explanation:

Answer 2

`y = 18 \cdot \left(8^x\right)`

Explanation:

The question is asking for an exponential function in the form
`y = a\cdot b^x`. The goal is to find the value of
`a` and
`b` such that both
`(0,\, 18)` and
`(3,\, 9216)` are on the graph of this function.

Saying that a point
`(m,\, n)` is on this function is the same as stating that if
`x = m`, then
`y = a \cdot b^m = n`.

• 
  `(0,\, 18)` is on
  `y = a\cdot b^x`. Therefore, when
  `x = 0`, it must be true that
  `y = a \cdot b^0 = 18`. On the other hand, any non-zero number to the
  `0`th power is
  `1`. Since (apparently)
  `b \\e 0`,
  `a \cdot b^0 = a`. Conclusion:
  `a = a \cdot b^0 = 18`.

• 
  `(3,\, 9216)` is on
  `y = a\cdot b^x`. Therefore, when
  `x = 3`, it must be true that
  `y = a \cdot b^(3) = 9216`. Since it is determined that
  `a = 18`,
  `18\, b^3 = 9216`. Hence
  `b^3 = 9216 / 18 = 512`. Take the cube-root of both sides:
  `b = \sqrt[3]{512} = 8`.

Conclusion:

• 
  `a = 18`.
• 
  `b = 8`.

Therefore,
`y = 18\cdot \left(8^x\right)`.