FORMULABANK

When plotting a growth function, typically the number of periods is represented along the x-axis, and the values of F_n are plotted on the y-axis.

Standard Formula for a Growth Function:

$f\left(x\right)=F_0·(1+r\%{)}^x$

When constructing the growth function, we aim to determine the account balance after any given number of periods. Therefore, x in the formula corresponds to the number of periods, and f(x) represents the final value. We do not substitute a specific number for x when creating the formula.

Instead, we insert a value for F₀ (the initial amount) and for the interest rate in the formula. See the example below:

Example:

Suppose we want to create a graphical representation of the development of 5 DKK in an account with a 10% interest rate over x number of years.

• Initial amount: F₀ = 5
• Interest rate: 10%

$f\left(x\right)=5·(1+\mathrm{10\%)}{}^{}$
x

This is entered into GeoGebra’s input field to plot the growth function.

Find Intersection with the Graph:

To determine how much money is in the account after 7 periods:

• Enter x = 7 in the input line
• Find the intersection between the vertical line and the graph
• Read the y-coordinate of the intersection, which is 9.74 (read in the algebra window).

Thus, after 7 periods, there are 9.74 in the account.