Question

The median house price in Waterloo Region increased by 3.6% from Jan 1, 2018 to Jan 1, 2019. A home

was purchased in Waterloo Region on April 1, 2019 for $600,000.

(a) Assume this trend continues, write an exponential equation that models the Resale Value of this
home over time.

(b) At this rate, determine the date of the resale price of the home would reach $1 million (Show your
work to accurate to the nearest month)

(c) Use your exponential equation to determine the expected resale value of the home on April 1, 2020.

Answer 1

The right answer is:

(a)
`P(t) = P_o \ e^(0.03536t)`

(b)
`t = 14 \ years \ 6 \ months`

(c)
`P(t) = =621,595.6` ($)

Explanation:

Given:

House price increment rate,

= 3.6% annually

(a)

Let the exponential equation will be:

⇒
`P(t) = P_o e^(Kt)`

here,

t = 0

P = P₀

t = 1 yr

then,

`P(1) = P_o +3.6 \ persent \ P_o`

`=1.036 \ P_o`

now,

⇒
`1.036 P_o = P_o \ e^(K.1)`

`ln(1.036) = K`

`K = 0.03536`

Thus, the exponential equation will be "
`P(t) = P_o \ e^(0.03536t)`".

(b)

We know,

`P_o = 600,000` ($)

`P(t) = 10,00,000` ($)

∵
`P(t) = P_o \ e^(0.03536t)`

`1000000=600000 \ e^(0.03536 t)`

`(5)/(3)= e^(0.03536 t)`

`ln((5)/(3) )=0.03536 t`

`((0.5)/(0825) )/(0.03536) =t`

`t = 14.45 \ years`

or,

`t = 14 \ years \ 6 \ months`

(c)

`P_o=600,000` ($)

`t = 1 year`

Now,

⇒
`P(t) = P_o \ e^(0.03536 t)`

`=600000 \ e^( 0.03536* 1)`

`=621,595.6` ($)