Suppose that a jacket cost $100 in the year 2017. Then it takes 56 years for the jacket to cost $400
Given :
the cost of an item increases by 2.5% each year
A jacket cost $100 in the year 2017.
Lets frame the equation to find cost of Jacket for 't' years
we need to find out 't' when cost is 400 dollars
Apply the formula
[tex]FV=PV(1+r)^t[/tex]
PV (present value ) is the initial cost=100
FV ( future value ) is the cost after 't' years= 400
r is the rate of increase =2.5%= 0.025
t = number of years taken
Replace all the values inside the formula
[tex]FV=PV(1+r)^t\\400=100(1+0.025)^t\\Solve \; for \; t\\divide \; both \; sides \; by \; 100\\4=(1+0.025)^t\\[/tex]
Now take ln on both sides to move exponent 't' down
[tex]4=(1+0.025)^t\\\\ln(4)=ln(1+0.025)^t\\\\ln(4)=t ln(1.025)\\divide \; both \; sides \; by ln(1.025)\\t=\frac{ln(4)}{ln(1.025)} \\t=56.14206[/tex]
It takes 56 years for the jacket to cost $400
Learn more : brainly.com/question/13734224
