v(x) = 32000/ (x/5 + 1)^2
average annual price change for the first 5 years
= (v(5) - v(0) )/(5-0)
= 32000/ (x/5 + 1)^2)
= (32000 / (1+1)^2 - 32000/(0+1)^1 )/5
= (8000-32000)/ 5 = -4800 , the negative shows me the value is decreasing
b) v ' (x) = -64000(x/5 + 1)^-3 (1/5)
= -12800/(x/5 + 1)^3
v ' (5) = -12800/(1+1)^3 = - 1600
Can someone help me!
3. The value of a car (in $), 𝑥𝑥years after it is purchased, is given by:
v(x) = 32000/(((x/5)+1)^2)
a) What is the average annual price change for the first 5 years?
b) What is the instantaneous rate of change of 𝑉 when 𝑥 = 5 ?
2 answers
v(x) = 32,000 / { (x/5)+1}^2
v(0) = 32,000
v(5) = 32,000/ { (5/5)+1}^2 = 32,000 / 4 = 8,000
change over five = 24,000
average = 24,000 / 5 = 4,800/year
dV/dx = -32000 * 2 { (x/5)+1}{1/5} / { (x/5)+1}^4
when x = 5
dV/dx = 6400 {2}{1/5}/ 8 =320
v(0) = 32,000
v(5) = 32,000/ { (5/5)+1}^2 = 32,000 / 4 = 8,000
change over five = 24,000
average = 24,000 / 5 = 4,800/year
dV/dx = -32000 * 2 { (x/5)+1}{1/5} / { (x/5)+1}^4
when x = 5
dV/dx = 6400 {2}{1/5}/ 8 =320