(1, 7.5) on our graph means if we plug in 1 for x we will get 7.5 for y.
7.5 = a×b¹
7.5 = a×b
(3, 16.875) means plugging in 3 for x gets us 16.875 for y.
Let's do some substitution.
16.875 = a×b³
16.875 = a×b×b×b
16.875 = (a×b)×b×b
16.875 = 7.5×b×b
2.25 = b²
1.5 = b
Try solving for a now.
7.5 = a×1.5¹
7.5 = a×1.5
5 = a
Here is our final equation:
[tex]\boxed{y=5*1.5^x}[/tex]
