Answer:
Step-by-step explanation:
The formula for calculating exponential decay is expressed as
A = P(1 - r)^t
where
A is the price after t years
P is the initial price
r is the rate of decay
t is the number of years
From the information given
P = 42000
r - 12% = 12/100 = 0.12
By the time it is half of its initial price, A = 42000/2 = 21000
By substituting these values into the formula, we have
21000 = 42000(1 - 0.12)^t
21000/42000 = (0.88)^t
0.5 = (0.88)^t
Taking natural log of both sides,
ln 0.5 = tln0.88
t = ln0.5/ln0.88
t = 5.44
The closest option is 6
Thus,
time = 6 years