Use Multiplication Properties of Exponents · Exercise 80

Clearance A department store is clearing out merchandise in order to make room for new inventory. The plan is to mark down items by 30% each week. This means that each week the cost of an item is 70% of the previous week’s cost. If the original cost of a sofa was $1,000, the cost for the first week would be \ 1,000 \left(0.70\right)$andthecostoftheitemduringthesecondweekwouldbe$$ 1,000 \left(0.70\right)^{2}$. Complete the table shown below. What will be the cost of the sofa during the fifth week? Simplify the expression, to show the cost in dollars.

\begin{array}{|c|c|}\hline \text{Week} & \text{Cost} \\ \hline \text{1} & \\text{ 1,000 left(0.70right)$} \\ \hline \text{2} & \\text{ 1,000 left(0.70right)^2$} \\ \hline \text{3} & \\ \hline \text{4} & \text{…} \\ \hline \text{5} & \text{?} \\ \hline\end{array}

This problem refers to a figure in its source book that isn't reproduced here.

OpenStax, Elementary Algebra 2e · §6.2 Use Multiplication Properties of Exponents · Exercise 80