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) = 0.15e0.20t million dollars, where t is the number of years since 2000. For the 4-plex in 2010, how fast in dollars was it increasing per year? Enter your answer without the dollar sign. (Ex: 456,000 would be entered for $456,000)

221,672

Explanation:

To find the rate of increase, find differential of p (t)

p (t) = 0.15e^ (0.2t)

dp/dt = 0.03e^ (0.2t)

at t=10

dp/dt = 0.03e^ (0.2*10)

dp/dt = 0.03e^2

dp/dt = 0.221672 million dollars

dp/dt = 221,672

221,672

Explanation:

This can be calculated by first finding the derivative of p (t) = 0.15e^0.20t. This done by differentiating the p (t) with respect to t as follows:

Given p (t) = 0.15e^0.20

p' (t) = (0.15e^0.20t) * (0.20) = 0.03e^ (0.20t) ... (1)

Number of years, i. e. t, is the difference between 2010 and 2000. Therefore,

t = 2010 - 2000 = 10

Substituting t = 10 into equation (1), we have:

p' (t) = 0.03e^ (0.20 * 10) = 0.03e^2 ... (2)

Since e^2 = 7.38905609893065, we substitute it into equation (2) as follows:

p' (t) = 0.03 * 7.38905609893065 = 0.22167168296792

Since it is in million dollars, we multiply it by 1,000,000 as follows:

p' (t) = 0.22167168296792 * 1,000,000

p' (t) = 221,672 approximately

Therefore, the 4-plex in 2010 was increasing by 221,672 dollars per year.