(1,2) , (3,50) Write an exponential function y=ab^x whose graph passes through the given points.

The given two points of the exponential function are (1,2) and (3,50).
To determine the exponential function
y=ab^x
plug-in the given x and y values.
For the first point (1,2), plug-in x=1 and y=2.
2=ab^1
2=ab          (Let this be EQ1.)
For the second point (3,50), plug-in x=3 and y=50.
50=ab^3       (Let this be EQ2.)
To solve for the values of a and b, apply substitution method of system of equations. To do so, isolate the a in EQ1.
2=ab
2/b=a
Plug-in this to EQ2.
50=ab^3
50=(2/b)b^3
And solve for b.
50=2b^2
50/2=b^2
25=b^2
+-sqrt25=b
+-5=b
Take note that in the exponential function y=ab^x , the b should be greater than zero (bgt0) . When blt=0 , it is no longer an exponential function.
So consider only the positive value of b which is 5.
Then, plug-in b=5 to EQ1.
2=ab
2=a(5)
Isolate the a.
2/5=a
Then, plug-in a=2/5 and b=5 to
y=ab^x
So this becomes:
y=2/5*5^x
Therefore, the exponential function that passes the given two points is y=2/5*5^x .