Find an exponential function of the form f(x)=ba^x or f(x)=ba^x+c. With the given points. (1,5) (0,2). The graph is increasing from quadrant 2 to quadrant 1?

1 Answer
Mar 12, 2018

# f(x) = 2 (5/2)^x #

Explanation:

If we have:

# f(x) = ba^x+c #

Then we have three unknowns but only two coordinates, which would lead to an inconsistent system of equations.

Therefore, we must consider a solution of the form:

# f(x) = ba^x #

Then we require that #y=f(x)# passes through the first point #(1,5)#, so that:

# f(1) = 5 => ba = 5 #

And also the second point #(0,2)#, so that:

# f(0) = 2 => b = 2#

Substituting this value of #b# in the first equation we establish:

# 2a = 5 => a = 5/2 #

Hence we gain the solution:

# f(x) = 2 (5/2)^x #

Which we can graph as follows:
graph{2(5/2)^x [-8, 5, -5, 8]}