Need help with exponential functions

Ok, so the function form is y = a * b^x.

Substitute in the values:

750 = a * b⁵

and

48 = a * b²

Then divide the two equations:

750/ 48 = (a * b⁵) / (a * b²)

So: 

15.625 = b³

Take the cube root of both sides:

2.5 = b

Now, substitue b into one of the equations (the one with 48 has smaller numbers and is easier to work with.)

48 = a * 2.5²

Simplify.

48 = a * 6.25

Divide both sides by 6.25

7.68 = a

Now substitute in a and b to write the exponential function: 

y = 7.68 * 2.5^x

Using the first equation we can "solve" for "a'

48/b^2 = "a"      (A)

And substituting this for "a" into the second equation, we get...

750 = (48/b^2)b^5    Divide both sides by 48 and simplify the exponents

750/48 = b^3   .....take the cube root of both sides.... 

"b"= 2.5

And using (A) and substituting in for "b," we have

48/(2.5)^2 = "a" = 7.68 

So....our equation is

y = 7.68(2.5)^x

Check and make sure it works....I'll think you'll find that it will.......

Sorry, kitty<3.....didn't know you were posting, too!!

I'll give you the credit with a "Thumbs Up" and a green check!!

Oh, it's fine:) Thanks!

Thumbs up to both of you so much work and problems in there #HULK FINGERS

Just one final thing....kitty<3 and I took completely different approaches to this.....

It just proves that there might be more than one way to produce the same solution!!