Posted by Jamie on Tuesday, June 17, 2014 at 9:52am.
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.
a) Write a differential equation that models this situation. Let V represent the value of the home (in thousands of dollars) and t represent the number of years since its value was $240,000.
For this, I got dV/dt = kV but I'm not positive it's correct. I also need to solve for the particular solution in terms of V and t and I'm not sure how to do that.
Calculus - Damon, Tuesday, June 17, 2014 at 10:19am
dV/dt = k V
dV/V = k dt
ln V = k t + C
e^ln V = V definition of ln
V = e^(kt + C)
C is arbitrary so far
V = e^kt * e^C
= C e^kt since e^c could be any old C
Now that is general solution. Now put in t = 0
at t = 0 e^kt = e^0 = 1
240,000 = C e^0 = C
V = 240,000 e^kt
Now if t = 2, V = 235,000
235 = 240 e^2k
e^2k = .979
ln e^2k = 2k = -.02105
k = - .010526
V = 240,000 e^-.010526 t
Calculus - Jamie, Tuesday, June 17, 2014 at 10:26am
If the question says to write the differential equation "in thousands of dollars" would the particular solution be written as V(t)=240e^((-.010526)(t)) instead of V = 240,000 e^-.010526 t ?
Calculus - Damon, Tuesday, June 17, 2014 at 10:29am
sure, in fact I did it with 235 = 240 e^2k
Calculus - Jamie, Tuesday, June 17, 2014 at 10:34am
The last question for this problem asks to find the relative rate of change in the home's value at any time t. How would I do that?
Calculus - Damon, Tuesday, June 17, 2014 at 11:37am
You have dV/dt = k V
and you know that k = -.010526
Calculus - Jamie, Tuesday, June 17, 2014 at 11:50am
So would it be -.010526 = (dV/dt)/V ?
Calculus - Damon, Tuesday, June 17, 2014 at 12:08pm
I suppose :)
Answer This Question
More Related Questions
- calculus - writing an exponential equation The function gives the value of a ...
- College Algebra - A cars value is declining exponentially. The car is currently ...
- Algerbra 2 - alex buys a home for 118000. her home increases in value 9% each ...
- personal finance - Katherine Kosher has determined the following information ...
- Math - The home that you purchased in 2004 steadily increased in value for the ...
- Finance - If a home buyer purchases a home in 2006 for $225,000 with a 10% down ...
- Algebra I - Please show me how to solve: The value of a $20,000 car decreases ...
- differential calculus - A bulldozer costs $120,000 and each year it depreciates ...
- math - The table shows the median home prices in Florida. What is the equation ...
- math - The value of a $20,000 car decreases every year, t. The equation below ...