Areal estate office manages an apartment complex with 50 units. when the rent is $780 per month, all 50 units are occupied. however, when the rent is $825, the average number of occupied units drops to 47. assume that the relationship between the monthly rent p and the demand x is linear (note: the term demand refers to thenumber of occupied units.)
(a) write a linear equation giving the demand x in terms of the rent p. (b) linear extrapolation - use a graphing utility to graph the demand equation and use the trace feature to predict the
number of units occupied when the rent is raised to $855. (c) linear interpolation - predict the number of units occupied when the rent is lowered to $795.

A) The linear equation is

B) When the rent is raised to $855 the number of units occupied is 45.

C) When the rent is lowered to $795 the number of units occupied is 49.  

Step-by-step explanation:

A) A linear equation for the demand is written as , where is the slope, is the number of occupied units, is the rent.

is calculated using the problem information. When the rent is then and when the rent is then .

Using the slope equation we have:

Thus the linear equation is:

In order to calculate we use the problem information, When the rent is then number of occupied units is , thus:

Finally, the linear equation is:

B) The demand equation is plot in the attached file, the number of units occupied when the rent is raised to $855 is 45.

C) In order to predict the number of occupied units lets use the equation:

where , then:

Thus, when the rent is lowered to $795 the number of units occupied is 49.  

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step-by-step explanation: