How to Model Currency Value Halving Every 4 Years During War?

What function will accurately model the situation where a country's currency loses half its value every 4 years due to inflation, especially during wartime?

A) C(t) = 1.36 * (0.5)^(t/4)
B) C(t) = 1.36 * (2)^(t/4)
C) C(t) = 1.36 - 0.5t
D) C(t) = 1.36 / (0.5t)

Final Answer:

To model a currency's value halving every 4 years due to inflation, especially during wartime, use the exponential decay function C(t) = 1.36 * (0.5)^(t/4).

Explanation: In this scenario, the equation that accurately models the situation where a country's currency loses half its value every 4 years due to inflation, particularly during wartime, is A) C(t) = 1.36 * (0.5)^(t/4). Here, C(t) represents the value of the currency at any given time 't' in years. The value '1.36' denotes the initial average currency exchange rate, '0.5' signifies the halving of the currency's value, 't' represents the time in years, and the factor '4' in the exponent 't/4' reflects the 4-year period over which the currency's value halves.

It is essential to use an exponential decay function in this context because it accurately captures the gradual decrease in the currency's value over time due to inflation, especially in the volatile environment of wartime. By utilizing the equation C(t) = 1.36 * (0.5)^(t/4), you can effectively model how the currency's value halves every 4 years, allowing for strategic financial planning and analysis during periods of economic instability.