Explanation:
The formula for continuous compounding is given by:
A = Pe^(rt)
Where:
A = the final amount of the investment
P = the initial principal amount
e = the mathematical constant (approximately equal to 2.71828)
r = the annual interest rate as a decimal
t = the number of years the investment is held
For this problem, P = $100, r = -0.08 (since the value of the investment is decreasing), and t = the number of years.
Therefore, the formula for the value of the investment after t years is:
A = 100e^(-0.08t)
For example, if we want to find the value of the investment after 5 years:
A = 100e^(-0.08*5) = $67.98
So, after 5 years, the initial investment of $100 would be worth approximately $67.98.