Final answer:
To solve for the unknown number of years, we first identify the unknown variable, find the known values, and use the appropriate equation to solve for the unknown. This method can be applied in financial contexts with simple interest calculations or in growth scenarios where a base increase is given.
Step-by-step explanation:
Solving for the Unknown Number of Years
To solve for the unknown number of years, we need to identify the unknown, recognize the knowns, and select an appropriate equation to substitute the knowns and solve for the unknown. For instance, in a scenario where the future amount is three times the original and the base increase is 1.05 per year, we can use the equation mentioned to find that n is 22.5 years. However, if we change the base to 2, the equation would yield n = 1.58, which implies that it will take 1.58 doubling times or approximately 22.5 years for the scale to reach three times the initial value.
In cases involving simple interest, we bring two formulas together to calculate the total future amount. For example, if we apply the simple interest formula over three years, we can determine the total accrued amount at the end of that time period.