The median value of a home in a particular market is decreasing exponentially. If the value of a home was initially $240,000, then its value two years later is $235,000. Answer the following.

1) Determine when the value of the home will be 90% of its original value.

Would the equation be set up like so: V=240e^.09t?

2) Determine the rate at which the value of the home is decreasing one year after it is valued at $235,000. Include units in your answer, and round the final value to the nearest dollar.

What I know so far: V=240e^ (-0.01052) t

Would you make t=1 and v=235?

3) The relative rate of change in a quantity is defined as the rate of change for that quantity divided by the quantity present. Find the relative rate of change in the home's value at any time t.

I know that it will be dV/dt=VK

I know k=-0.01052, would the final answer be - 0.-1052 = (dV/dt) / V

1st let's calculate the decreasing rate & let V₁ be the initial value & V₂ the final's

we know that V₂=V₁. e^ (r, t) where r=rate & t-time (& e=2.718)

After t = 2 years we can write the following formula

2350,000=240,000. e^ (2r) = = > 235,000/240000 = e^ (2r) = >47/48=e^ (2r)

ln (47/48) = 2rlne==> ln (47/48) = 2rlne=2r (since lne = 1)

r = ln (47/48) / 2==>r=-0.0210534/2 = - 0.01052 = = > (r=-0.01052)

1) Determine when the value of the home will be 90% of its original value.

90% of 240000 = 216,000

Now let's apply the formula

216,000=240,000, e^ (-0.01052t), the unknown is t. Solving it by logarithm it will give t=10 years

1. a) Would the equation be set up like so: V=240e^.09t? NON, in any case if you solve it will find t=1 year

2) Determine the rate at which the value of the home is decreasing one year after : Already calculated above : (r=-0.01052)

3) The relative rate of change : it's r = - 0.01052