Question

N 2008 price of houses were declining by 2% each year. If a house was purchased for $195,000, write the equation that models the situation.

Answer 1

p₁ = 0.98 p₀

p₂ = 0.98 p₁

Explanation:

Given - N 2008 price of houses were declining by 2% each year.

If a house was purchased for $195,000.

To find - Write the equation that models the situation.

Proof -

Let us assume that

p₀ = initial price of house

p₁ = price of house after 1 year

p₂ = price of house after 2 years

Now,

Given that, p₀ = $195,000

Then,

p₁ = p₀ - 2% p₀

= p₀( 1 - 2%)

= p₀ ( 98%)

⇒p₁ = 98% p₀

⇒p₁ =
`(98)/(100)` p₀

⇒p₁ = 0.98 p₀

Now,

Also p₂ = p₁ - 2% p₁

By doing the same process as above, we get

p₂ = 0.98 p₁