Questions: A real estate investor researches 4-plex apartment complexes in a city and finds that from 2000 to 2012, the average price of the 4-plex is approximated by p(t)=0.15 e^(0.2 t) million dollars, where t is the number of years since 2000.
For the 4-plex in 2010, how fast in millions of dollars was it increasing per year? Enter your answer to 3 decimal places.
t=10
To find the change of price of the 4-plex per year in 2010, we take the derivative of p. Set up the derivative of 0.15 e^(0.20 t) using prime notation.
Transcript text: A real estate investor researches 4-plex apartment complexes in a city and finds that from 2000 to 2012, the average price of the 4-plex is approximated by $p(t)=0.15 e^{0.2 t}$ million dollars, where $t$ is the number of years since 2000.
For the 4-plex in 2010, how fast in millions of dollars was it increasing per year? Enter your answer to 3 decimal places.
$t=10$
To find the change of price of the 4-plex per year in 2010, we take the derivative of $p$. Set up the derivative of $0.15 e^{0.20 t}$ using prime notation.
Solution
Solution Steps
Step 1: Derivative Calculation
To determine how fast the price of the 4-plex is increasing per year, we first calculate the derivative of the price function p(t)=0.15e0.2t. The derivative is given by:
p′(t)=0.03e0.2t
Step 2: Evaluate the Derivative at t=10
Next, we evaluate the derivative at t=10 (which corresponds to the year 2010):
p′(10)=0.03e0.2⋅10=0.03e2≈0.221671682967920
Final Answer
The rate of increase in the price of the 4-plex in 2010 is approximately 0.222 million dollars per year. Thus, we can express the final answer as: