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.]

Question

Mathematics

Frida Shaffer

18 June, 14:11

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.]

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Heidi Shepard · 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