If f(x) is an exponential function where f(4.5) = 24 and f(14.5) = 54, then find the value of f(6.5), to the nearest hundredth.

The value of is 28.22.

Step-by-step explanation:

The exponential function is modelled after this model:

(1)

Where:

- Coefficients.

- Independent variable.

- Dependent variable.

By using all information from statement, we have the following system of equations: ,

(2)

(3)

By dividing (3) by (2), we calculate :

If we know that and , then the value of is:

If we know that , then the value of is:

(4)

The value of is 28.22.

7

step-by-step explanation:

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is