Question

Tell whether it shows growth or decay and graph by using a table of values

Answer 1

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given exponential function

`f(x)=0.5^x`

STEP 2: Compare with the standard exponential function to determine whether it shows growth or decay.

If a is positive and b is greater than 1 , then it is exponential growth.

If a is positive and b is less than 1 but greater than 0 , then it is exponential decay.

`\begin{gathered} f(x)=a\cdot b^x_{} \\ \text{Comparing with }f(x)=0.5^x,\text{ it can be written as }f(x)=1*0.5^x, \\ It\text{ can be se}en\text{ that }a=1,b=0.5 \\ \text{ Since }a\text{ is positive and b is less than 1 but greater than 0, then it is an exponential decay.} \end{gathered}`

Hence, the given function shows an exponential decay.

STEP 3: Graph the values by using a table of values

We generate a table of values first

STEP 4: Plot the graph of the data values