FORMULABANK

When drawing a growth function, one typically places the number of periods on the x-axis and the values of K_n on the y-axis.

Standard formula for a growth function

$f\left(x\right)=k_0·(1+r\%{)}^x$f(x)=k_0*(1+r%)^n

When creating a growth function, one wants to be able to read the value in the account after any number of periods. Therefore, x in the formula corresponds to the number of periods and f(x) corresponds to the final value. Thus, we do not substitute a number for x when forming the function.

Instead, we insert a value in the place of K₀ and in the position of the interest rate in the formula. See below.

Example:
If we want to create a graphical representation of the development of 5 kroner in an account with an interest rate of 10% for x number of years.
Then K₀ = 5 and the interest rate = 10%
f(x)=5·(1+10%)^x  Entered in GeoGebra’s input field

Finding the intersection with the graph:

If one wants to determine how much money is in the account after 7 periods.

Write x = 7 in the input line → Find the intersection point between the vertical line and the graph → Read the y-coordinate of the intersection point, which here is 9.74 as shown in the algebra window.

That is, after 7 periods there are 9.74 kroner in the account.