Math word problem

Question

The number of houses that are unoccupied has grown approximately exponentially from 8.5 million in 1980 to 14.3 million in 2010. Predict the number of houses that will be unoccupied in 2020

Answer 1

Let y = the number of houses that are unoccupied at time t.  The general form of exponential growth is:

 

     y = a*b^t

 

where:

• a = the initial number of unoccupied houses (1980) = 8.5 million
• b = the rate
• t = years since 1980

 

In 2010, we have 14.3 million unoccupied homes.  Let's use that to find the value of b:

 

     y = a*b^t

     14.3 = 8.5*b^(2010-1980)

     14.3/8.5 = b³⁰

     (1.6824)^1/30 = b

     1.0175 = b

 

So the full equation is:

 

     y = 8.5*(1.0175)^t

 

To find the value of y in 2020, plug in t = 2020-1980 = 40