Exponential Function
The situation explained in the question will be modeled with an exponential function of the form:
[tex]v(n)=a\cdot b^n[/tex]
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:
[tex]\begin{gathered} 100=a\cdot b^0 \\ 100=a\cdot1 \\ \text{Solve for a:} \\ a=100 \end{gathered}[/tex]
Now the function is:
[tex]v(n)=100\cdot b^n[/tex]
We also know v(1)=500. Substituting:
[tex]\begin{gathered} 500=100\cdot b^1 \\ 500=100\cdot b \\ \text{Divide by 100:} \\ b=\frac{500}{100}=5 \end{gathered}[/tex]
The function is now complete:
[tex]v(n)=100\cdot5^n[/tex]
