Answer
(a) $P_n=(1.06)^n P_0=240000\times(1.06)^n $
(b) $382523.54$ dollars.
Work Step by Step
(a) Step 1. The starting price is $P_0=240000$,
Step 2. For the first year, with $6\%$ increase, the price will be $P_1=1.06P_0$,
Step 3. For the second year, there will another $6\%$ increase so that $P_2=1.06P_1=(1.06)^2P_0$... ...
Step 4. After n-years, the price will be $P_n=1.06P_{n-1}=(1.06)^2P_{n-2}= ... =(1.06)^n P_0$,
Step 5. The answer is $P_n=(1.06)^n P_0$
(b) 2010 will correspond to 8 years after 2002, thus $n=8$ and $P_8=(1.06)^8 \times 240000=382523.54$ dollars. The results for up to 12 years are shown in the figure.
