Ayoung couple purchases their first new home in 2002 for $120,000. they sell it to move into bigger home in 2007 for $150,000. first, we will develop an exponential model for the value of the home. the model will have the form v(t)=v0ekt. let t be years since 2002 and v(t) be the value of the home.

The exponential model for the value of the home is .

Step-by-step explanation:

According to the give information 2002 is the initial year and the value of the hom in 2002 is $120,000.

The model will have the form

Where V₀ is initial value of home, k is a constant and t is number f years after 2002.

The value of home in 2007 is $150,000. Difference between 2007 and 2002 is 5 years. Therefore the value of function is 150000 at t=5.

Take ln both sides.

                   ()

Therefore exponential model for the value of the home is .

Where t is number of years after 2002.

Step-by-step explanation:

If the given equation is                .............(i)

Here from the question it is given that

V(t) = $150,000

V₀=$120,000

t= 2007-2002=5 years

e≅2.718

k=?

Now for the Value of k putting all values in equation (i)

Now taking Natural log on both sides of the equation

㏑ (e^{5(k)})= ㏑\frac{5}{4}

as we Know that ln(e)=1

so

5k = 0.223

dividing both sides by 5 gives

k =

k= 0.044

Now as we got the value of k we can form a general exponential equation which will be

here value of v₀ is 120000

so equation will be