Question

The average price of a two-bedroom apartment in the uptown area of a prominent American city during the real estate boom from 1994 to 2004 can be approximated by p(t) = 0.15e0.10t million dollars (0 ≤ t ≤ 10) where t is time in years (t = 0 represents 1994). What was the average price of a two-bedroom apartment in this uptown area in 2002, and how fast was it increasing? (Round your answers to two significant digits.) HINT [See Quick Example 3.]

Answer 1

p(t) = 0.19e0.10t

=>p'(t) = 0.19e0.10t (0.10*1)

=>p'(t) = 0.019e0.10t

t = 0 represents 1994

for 2002, t=2002-1994 =8

in 2002

average price =p(8)

=>average price = 0.19e0.10*8

=>average price =0.422853... million

rate of increase =p'(8)

=>rate of increase = 0.019e0.10*8

=>rate of increase =0.0422853... million per year

p(8)=$ 0.42 million

p'(8)=$ 0.042 million per year