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. 6) 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. 7) Solve for the particular solution in terms of V and t (find the values of all constants). 8) Determine when the value of the home will be 90% of its original value.
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. 6) 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. 7) Solve for the particular solution in terms of V and t (find the values of all constants). 8) Determine when the value of the home will be 90% of its original value.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text: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.
6) 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.
7) Solve for the particular solution in terms of V and t (find the values of all constants).
8) Determine when the value of the home will be 90% of its original value.
9) 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.
10) 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.
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