Question

Find an exponential function, algebraically, of the form y=ab^x whose graph passes through the given points: (2,6)(4,150)

with work please!!

Answer 1

`y=(6)/(25)(5)^x` or
`y=0.24(5)^x`

Explanation:

You know two points, so make two equations:

`6=ab^2`

`150=ab^4`

Solving for
`a` in the first equation, we have
`\displaystyle a=(6)/(b^2)`, so this value can be plugged into the second equation to solve for
`b`:

`\displaystyle 150=ab^4\\\\150=\biggr((6)/(b^2)\biggr)b^4\\\\150=6b^2\\\\25=b^2\\\\5=b`

Thus, we can now find the value of
`a` given that
`b=5` using either equation (I'll use the first one since it's easier):

`\displaystyle 6=ab^2\\6=a(5)^2\\6=25a\\a=(6)/(25)=0.24`

Hence, the exponential function whose graph passes through the given points is
`\displaystyle y=(6)/(25)(5)^x`, or
`y=0.24(5)^x`. I've attached a Desmos graph, and the regression confirms this answer is correct.