Answer:
About 3.73 yrs
Step-by-step explanation:
This is a compound decay problem. Which has the formula:
[tex]F=P(1-r)^t[/tex]
Where
F is the future amount (we want it to be 2000)
P is the present amount (which is 4600)
r is the rate of decay, depreciation (20% per year means 20/100 = 0.2)
t is the time in years (which we want to find)
Substituting, we find:
[tex]F=P(1-r)^t\\2000=4600(1-0.2)^t\\2000=4600(0.8)^t\\0.4348=0.8^t[/tex]
Now we take natural log (Ln) of both sides and solve:
[tex]Ln(0.4348)=Ln(0.8^t)\\Ln(0.4348)=tLn(0.8)\\t=\frac{Ln(0.4348)}{Ln(0.8)}\\t=3.73[/tex]
So, it will take about 3.73 years for the value to depreciate to $2000
Answer: 3.733
Step-by-step explanation: if it asks for thousandths
