Question

A government program that currently costs taxpayers $4.5 billion per year is cut back by 3% per year. Write an expression for the amount budgeted (in dollars) for this program after n years.

Answer 1

The expression for the amount budgeted for a government program after n years with a 3% annual cutback is $4.5 billion × (0.97)^n.

Step-by-step explanation:

To write an expression for the amount budgeted for a government program after n years with an annual cutback rate of 3%, we leverage the formula for exponential decay. The initial amount is $4.5 billion, and it decreases by 3% each year, which can be represented as multiplying the initial amount by 97% (or 0.97) each year. Therefore, the expression would be:

Amount after n years = $4.5 billion × (0.97)^n

This equation shows the exponential decay of the program budget over time, where n represents the number of years.