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

We need to find a and b

when x=1, y=7.5
when x=3, y=16.875

7.5=ab^1
7.5=ab
divide both sides by a
7.5/a=b

16.875=ab^2
divide both sides by a
16.857/a=b^2
square root both sides
√(16.875/a)=b

we have

√(16.875/a)=b
7.5/a=b
set equal to each other and solve for a
7.5/a=√(16.875/a)
squaer root both sides
56.25/(a^2)=16.875/a
multply both sides by  a^2
56.25=16.875a
divide both sides by 16.875
3.333333333333333=a
sub
7.5=ab
7.5=3.3333333333333b
divide both sides by 3.33333333
2.25=b

the equation is y=3.3333333333(2.5)^x