Question

a car lose half of its value during it's first year of usage and there after loses 8% of its value in each year.calculate its value at the end of three years

Answer 1

Let x be the initial value of the car, then the first year the new value of the car will be:

$x_1=x\cdot0.50._{}$

In the second year, the new value of the car will be:

$x_2=x_1(1-0.08)\text{.}$

After 3 years, the value of the car will be:

$x_3=x_2(1-0.08)\text{.}$

Therefore, in terms of its initial value, at the end of three years the value of the car will be:

$x_3=0.50x(1-0.08)^2.$

Answer: If x is the initial value, then at the end of three years the value of the car will be:

$x_3=0.50x(1-0.08)^2.$