Thread: Coming up with an exponential equation

I need to come up with an exponential equation which fulfils the following criteria;
-is an increasing function
-is concave up
-pass through the points (0,3) and (4,11)
-has a definite integral of 22 between x=0 and x=4.

Why are you so sure the exponential function has base ? We know the exponential function is increasing so the base >1.

Hello, asaver!

I need an exponential equation which fulfils the following criteria:
. . [1] is an increasing function
. . [2] is concave up
. . [3] pass through the points (0,3) and (4,11)
. . [4] has a definite integral of 22 between x=0 and x=4.

Because of the -intercept
. . you believe the function has the form:

But it could have the form: .


You had best begin with the general exponential function: .


[1] and [2] tells us that


[3] says and

. . We have: .

[4] gives us: .

We have three equations in three variables
. . Solve the system.