The answer is 8.25 years
The exponential function can be expressed as:
A = P * e^(kt)
A - the final amount
P - the current amount
k - the rate
t - time in years
If the final amount is the half of its current amount, then:
A = P/2
So,
A = P * e^(kt)
P/2 = P * e^(kt)
Divide P from both sides:
1/2 = e^(kt)
Logarithm both sides with natural logarithm:
ln(1/2) = ln(e^(kt))
ln(0.5) = kt * ln(e)
k = -0.084
-0.693 = -0.084 * t * 1
-0.693 = -0.084t
t = -0.693 / -0.084
t = 8.25 years
