Question

Write an exponential equation y=ab^x whose graph passes through the points (2,3) and (5,24)

Answer 1

passes (2,3)

`3 = a * {b}^(2)`

passes (5,24)

`24 = a * {b}^(5)`

observe

`{b}^(3) = \frac{a * {b}^(5) }{a * {b}^(2) } = (24)/(3) = 8 \\ b = 2`

substitute to first equation we get a=¾

so the equation is

`y = (3)/(4) * {2}^(x)`