Final answer:
To estimate the debt after 12 years, substitute t with 12 in the equation A = 19.5(0.979)^t, resulting in a debt of approximately $15.09 billion when rounded to the nearest hundredth.
Step-by-step explanation:
The student has asked to estimate the debt of Country M after 12 years given that it decides to reduce their $19.5 billion debt by a decay factor of 0.979 each year, which can be modeled by the exponential decay function A = 19.5(0.979)ᵗ. To find the debt after 12 years, we substitute t with 12 and calculate the final amount. Therefore, we perform the following calculation:
A = 19.5 × (0.979)^12
Using a calculator to evaluate the exponent:
A = 19.5 × 0.774
And then multiply:
A ≈ 15.093 billion dollars
When rounded to the nearest hundredth, the debt of Country M after 12 years would be approximately $15.09 billion.