Write an equation for an exponential function, in the form y=axb^x, whose graph passes through the coordinate points (1, 7.5) and (3, 16.875).

7.5 = a*b^1

16.875 = a* b^3

Divide the last equation by the former

16.875/7.5  = b^ (3-1)

2.25 = b^(2)

extract square root from both sides

b = 1.5

From 7.5 = a*b ⇒ a = 7.5/ (1.5) = 5

The requested function is y = 5 (1.5)^x