Question

A book store had a $780,000 in sales revenue in 2000 and $590,000 in 2011. Assuming a constant EXPONENTIAL annual rate of decrease, what is the predicted sales revenue for 2017

Answer 1

Answer:

The predicted sales revenue for 2017=$501,334.008

Explanation:

If something reduces at a constant rate over a specified period of time, then it can be represented using an exponential function as follows;

y=a(1-r)^x, or y=ab^x

where;

y=final sales revenue after the reduction

a=initial sales revenue before the reduction

1-b=reduction factor

x=time interval

In our case;

y=$590,000

a=$780,000

1-r=b=unknown

x=2011-2000=12 years

replacing;

590,000=780,000.b^12

b^11=590,000/780,000=0.756

b=0.756^(1/12)

b=0.977

r=1-0.977=0.023

Determine predicted sales revenue;

y=ab^x

y=sales revenue in 2017

a=sales revenue in 2011=$590,000

b=0.977

x=7 years

replacing;

y=590,000(0.977)^7

y=$501,334.008

The predicted sales revenue for 2017=$501,334.008