Question

4. Ms. Schopke is thinking of getting some newfurniture. A local consignment store priced somechairs she likes using the formula c(w) = 100(0.9)*to model the cost of the chairs w weeks afterthey've been on sale. Which of the following bestinterprets the parameters of this function?

Answer 1

The general exponential decay function is:

$y=a(1-r)^x$

where x and y are the variables, a is the initial value and r is the decay rate (as a decimal).

In the formula:

$c(w)=100(0.9)^w$

c(w) is the cost after w weeks (in dollars), $100 is the initial value and

1 - r = 0.9

1 = 0.9 + r

1 - 0.9 = r

0.1 = r

r as a percentage is 0.1x100 = 10%. Then, the price starts at 100 dollars and decrease by 10% off each week until they are sold.