Question 1129690
the formula to use is f = p * (1 + r) ^ t


f is the future value
p is the present value
r is the growth rate per year
t is the number of years


in 3 years, the car reduces 19% in value.


therefore, in 3 years, the value of the car is 13000 minus .19 * 3000 = 10530.


your frmula of f = p * (1 + r) ^ t becomes:


10530 = 13000 * (1 + r) ^ 3


divide both sides of this equation by 1000 to get:
10530 / 13000 = 1 + r) ^ 3
take the third root of both sides of this equation to get:
(10530 / 13000) ^ (1/3) = 1 + r
subtract 1 from both sides of this equation to get:
(10530 / 13000) ^ (1/3) - 1 = r
solve for r to get:
r = -.0678302482


that's your annual growth rate.


your formula becomes:


f = 13000 * (1 - .0678302482) ^ t


in 1 year, the value of the car is 13000 * (1 - .0678302482) ^ 1 = 12118.20677.
in 2 years, the value of the car is 13000 * (1 - .0678302482) ^ 2 = 11296.2258.
in 3 years, the value of the car is 13000 * (1 - .0678302482) ^ 3 = 10530.


the 3 year growth factor is (1 - .0678302482) ^ 3 = .81
the 1 year growth factor is (1 - .0678302482) ^ 1 = .9321697518


the formula to find the value of the car after t years is f = 13000 * (1 - .0678302482) ^ t


that formula can be graphed as shown below.
the formula to graph is y = 13000 * (1 - .0678302482) ^ x.
in the graph, y represents f and x represents t.


<img src = "http://theo.x10hosting.com/2018/112502.jpg" alt="$$$" >