Question

Country G decides to reduce their $3.5 billion debt by a decay factor of 0.99 each year. Write an exponential equation to model the debt after years. Provide your answer below:

A=

Answer 1

The exponential equation to model Country G's debt reduced by a decay factor of 0.99 each year is A = 3.5 × (0.99)^t, where A is the debt after 't' years, and 3.5 is the initial debt in billions.

Step-by-step explanation:

The question asks for an exponential equation to model the reduction of Country G's debt by a decay factor of 0.99 each year. To write the equation, we start with the initial debt which is $3.5 billion and multiply it by 0.99 raised to the power of the number of years, 't'. This leads to the following equation:

A = 3.5 × (0.99)^t

Where:

• A is the amount of debt remaining after 't' years.
• 3.5 represents the initial debt in billions of dollars.
• 0.99 is the decay factor, indicating a 1% reduction of the remaining debt per year.
• 't' stands for the number of years that have passed.

For example, to calculate the debt after 1 year, we would plug in 't' as 1:

A = 3.5 × (0.99)^1

For 't' equals 2 years, the calculation would be:

A = 3.5 × (0.99)^2

And so on for subsequent years. Note that this model assumes that the percentage reduction remains constant and that there are no additional deficits or surpluses in the subsequent years.