How to calculate exponential function passing through the points

Question

When writing the formula for an exponential function passing through the points (−2,4/9) and (2,36) using the form y = ab^x , what would be the base, b?

Answer 1

We have two equations and two unknowns, so we can solve for both a and b

For equation 1)

y = ab^x

⁴/₉ = ab^-2

⁴/₉ * b² = a

For equation 2)

y = ab^x

36 = ab²

36b^-2 = a

Now set the two equations equal to each other and solve for b

⁴/₉ * b² = 36b^-2