Question

Find a formula for the exponential function passing through the points( -3, 1/32) and (1,8)

Answer 1

Explanation:

The equation of a exponential function is

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

Where a is the y intercept

and b is the multiplicative factor.

We know that

`(1)/(32) = a(b) {}^( - 3)`

`8 = a(b) {}^{}`

If we divide these two equations,

`(8)/( (1)/(32) ) = \frac{a * {b}^( - 3) }{a(b)}`

`256 = b {}^( - 4)`

`b = 4`

So know that we know b, plug it in one of the expressions to solve for a.

`8 = a( 4)`

`a = 2`

So, our function is

`y = 2(4) {}^(x)`