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.

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- July 25th 2011, 03:06 AMasaverDefinite Integrals
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. - July 25th 2011, 03:45 AMSironRe: Coming up with an exponential equation
Why are you so sure the exponential function has base ? We know the exponential function is increasing so the base >1.

- July 25th 2011, 05:51 AMSorobanRe: Coming up with an exponential equation
Hello, asaver!

Quote:

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.