Problema Solution
The function h(t)=15,000*(1.5)^t models the value of Sam's house, where t represents the number of decades since 1960. The value of Kendra's house has been doubling each decade since 1980. In 2010, the value of Sam's house was greater than the value of Kendra's house. Is it possible that the two houses had equal values in 1980? Explain.
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The cost of Sam's house in 1980 was:
h(2) = 15,000*(1.5^2) (t = 2 since there are 2 decade from 1960 till 1980)
h(2) = $33,750
The cost of Sam's house in 2010 was:
h(5) = 15,000*(1.5^5) (t = 5 since there are 5 decades from 1960 till 2010)
h(5) = $113,906.25
Lets assume that Kendra's house was worth $33,750 in 1980.
In 2010 the value of Kendra's house was: 33,750*2^3 = $270,000
Let's compare the values of the houses in 2010:
h(5) = $113,906.25 < $270,000
This means the value of Kendra's house is greater that the value of Sam's house. This is a contradiction follows it is not possible that the two houses had equal values in 1980.