Chapter 8, Problem 8CT

To determine

To check: Given table is linear, quadratic or exponential

Answer to Problem 8CT

Exponential function

  $f(x)=8{(2)}^x$

Explanation of Solution

Given information: A table with x and y values.

Calculation: To determine whether the table represents linear, quadratic or exponential, we need to analyze the y values

We can see that the y values are multiplied by 2 to get the next y value

  $\begin{array}{l}4\cdot 2=8\\ 8\cdot 2=16\\ 16\cdot 2=32\end{array}$

There is a common multiplier 2. So it’s an exponential function

The exponential function is of the form

  $y=a{(b)}^x$

Lets pick any two values from the table and solve for a and b

  $\begin{array}{l}(0,8)\\ y=a{b}^x\\ 8=a{b}^0\\ a=8\end{array}$

  $\begin{array}{l}(1,16)\\ y=a{b}^x\\ 16=8(b^1)\\ 16=8b\\ b=2\\ $ y=8{(2)}^x$\end{array}$

The function is exponential function is $f(x)=8{(2)}^x$