Question

Three years after purchase, a car is estimated to be worth

Answer 1

Y - value
x - year

$24000=a\cdot3+b\\ 19000=a\cdot5+b\\\\ 24000=3a+b\\ -19000=-5a-b\\ ---------\\ 5000=-2a\\ a=-2500\\\\ b+3\cdot(-2500)=24000\\ b-7500=24000\\ b=31500\\\\ \boxed{y=-2500x+31500}$

a)
$f(x)=-2500x+31500\\ f(x+1)=-2500(x+1)+31500\\ f(x+1)=-2500x-2500+31500\\ f(x+1)=-2500x+29000\\\\ f(x)-f(x+1)=-2500x+31500-(-2500x+29000)\\ f(x)-f(x+1)=-2500x+31500+2500x-29000\\ f(x)-f(x+1)=\boxed{2500}$

b)
$f(0)=-2500\cdot0+31500=\boxed{31500}$

c)
$f(10)=-2500\cdot10+31500\\ f(10)=-25000+31500\\ f(10)=\boxed{6500}$