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The median price, P, of a home rose from $50 thousand in 1980 to $150 thousand in 2000. Let t be the number of years since 1980. If instead the housing prices increased exponentially, find an equation of the form P = Poa t to represent housing prices. Again, P is measured in thousands. (Round your answer for a to 6 decimal places.)

Respuesta :

nobillionaireNobley
150,000 = 50000a^20
a^20 = 150000/50000 = 3
a = 20th root of 3 = 1.056467

Required equation is P = 50000(1.056467)^t

Answer: [tex]P=50,000(1.056467)^t[/tex]

Step-by-step explanation:

Here the function that shows the price of home after t years,

[tex]P=P_0(a)^t[/tex]

Where,

[tex]P_0[/tex] is the initial price of home,

a is the growth factor,

t is the time.

Here, The Initial price of home,

[tex]P_0 = $ 50,000[/tex]

P = $ 150,000

Time since 1980, t = 20 years.

Thus, [tex]150,000=50,000(a)^{20}[/tex]

[tex]3=(a)^{20}[/tex]

[tex]a=(3)^{1/20} =1.05646730855\approx 1.056467 [/tex]

Thus, the complete function that shows the price of home after t years,

[tex]P=50,000(1.056467)^t[/tex]


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