Answer:
Step-by-step explanation:
We will utilize the exponential decay formula described as
A = P(1 - r/n)^(nt)
Where
A symbolizes the value after a time period t.
n refers to the timeframe for value loss calculation
t indicates the number of years.
P stands for the population value.
r indicates the rate of decrease.
Based on the provided data,
P = 23000
r = 8% = 8/100 = 0.08
n = 1
Thus, the exponential decay function fitting this situation is
A = 23000(1 - 0.08/n)^1)^ t
A = 23000(0.92)^t
If A = 15000, it follows that
15000 = 23000(0.92)^t
0.92^t = 15000/23000 = 0.6522
Taking logarithm of both sides to base 10
Log(0.92^t) = log(0.6522)
t log(0.92) = log(0.6522)
- 0.036t = - 0.1856
t = - 0.1856/- 0.036
We find t = 5 years rounded to the nearest year
