Question

Some values of functions​ f, g,​ h, and k are provided in the table below. Find a possible equation of each function. Verify your results with a graphing calculator table.

Theres 4 parts to this

Answer 1

The functions f, g, h and k are $f(x)=15\cdot 3^{x}$, $g(x) = 26\cdot 0.5^{x}$, $h(x) = 7\cdot 8^{x}$ and $k(x) = 280\cdot 0.143^{x}$, respectively.

How to model monotonous functions

A function is monotonous when is either increasing or decreasing for all value of $x$. A power function is a case of a monotonous function, whose model is defined below:

$y = y_{o}\cdot r^{x}$ (1)

Where:

• $y_{o}$ - Initial value
• $r$ - Increase rate
• $x$ - Independent variable
• $y$ - Dependent variable

Now we proceed to define each function:

Case 1 (f(x) - Initial value: 5, increase rate: 3)

$f(x)=15\cdot 3^{x}$ (2)

Case 2 (g(x) - Initial value: 26, increase rate: 0.5)

$g(x) = 26\cdot 0.5^{x}$ (3)

Case 3 (h(x) - Initial value: 7, increase rate: 8)

$h(x) = 7\cdot 8^{x}$ (4)

Case 4 (k(x) - Initial value: 280, increase rate: 0.143)

$k(x) = 280\cdot 0.143^{x}$ (5)

The functions f, g, h and k are $f(x)=15\cdot 3^{x}$, $g(x) = 26\cdot 0.5^{x}$, $h(x) = 7\cdot 8^{x}$ and $k(x) = 280\cdot 0.143^{x}$, respectively. $\blacksquare$

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