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
# f(1) = 5 => ba = 5 #
And also the second point
# f(0) = 2 => b = 2#
Substituting this value of
# 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]}