Question

Build a function to represent the situation. Use the drop-down menu.

Answer 1

Exponential Function

The situation explained in the question will be modeled with an exponential function of the form:

$v(n)=a\cdot b^n$

Where a and b are constants to be determined by using the values given in the table.

We know that v(0) = 100. Substituting in the function:

$\begin{gathered} 100=a\cdot b^0 \\ 100=a\cdot1 \\ \text{Solve for a:} \\ a=100 \end{gathered}$

Now the function is:

$v(n)=100\cdot b^n$

We also know v(1)=500. Substituting:

$\begin{gathered} 500=100\cdot b^1 \\ 500=100\cdot b \\ \text{Divide by 100:} \\ b=\frac{500}{100}=5 \end{gathered}$

The function is now complete:

$v(n)=100\cdot5^n$