Q:

The number of VHS movie rentals has declined since the year 2000 due to the popularity of DVDs, as the following table shows. The exponential regression equation was found to be y=9.92(0.8209)^x where x represents the number of years since 2000. Use the regression equation to predict the number of VHS movies in 2011.

Accepted Solution

A:
Answer: the number of VHS movie rentals in 2011 is expected to be 1.13 million.

The table was not provided, but it is not necessary since the exponential regression equation was provided.

The exponential regression equation is the exponential function that best fits the set of data and it is given in the form:
y = a · bˣ

where:
a = initial value of the model
b = exponential grow or decay
x = time passed from the beginning

In our case,
y = 9.92 · (0.8208)ˣ

where:
a = 9.92
b = 0.8208
Since 0 < b < 1 we have an exponential decay, confirming that the number of VHS is decreasing with time.

We can then use this equation to infer the number of VHS movies in 2011.
As a first thing, calculate how many years from the beginning (2000) would pass:
x = 2011 - 2000 = 11

Now, substitute this value in the equation:
y = 9.92 · (0.8208)¹¹
   = 1.13

In 2011 we can predict there will be only 1.13 million VHS movie rentals.