Exponential Functions:Question $1$ $\newline$ Each Saturday, a store reduces the price of any unsold item by $\newline$ $10$ \%. If an item was priced at $\newline$ $\$80$ , on Saturday of the first week it is marked down to $\newline$ $\$72$ . At the end of the second week, it drops to $\newline$ $\$64.80$ , and at the end of the third week the price is decreased to $\newline$ $\$58.32$ . If this continues for $10$ weeks, what should be the selling price for an item that was originally priced at $\newline$ $\$80$ ? $\newline$ Select one: $\newline$ $\$27.89$ $\newline$ $\$52.11$ $\newline$ $\$8.00$ $\newline$ $\$30.99$

Full solution

Q. Exponential Functions:Question

1

\newline

Each Saturday, a store reduces the price of any unsold item by

\newline

10

\%. If an item was priced at

\newline

\$80

, on Saturday of the first week it is marked down to

\newline

\$72

. At the end of the second week, it drops to

\newline

\$64.80

, and at the end of the third week the price is decreased to

\newline

\$58.32

. If this continues for

10

weeks, what should be the selling price for an item that was originally priced at

\newline

\$80

\newline

Select one:

\newline

\$27.89

\newline

\$52.11

\newline

\$8.00

\newline

\$30.99

Identify price and markdown: Step $1$ : Identify the initial price and the weekly markdown percentage. $\newline$ Initial price = $\$80$ $\newline$ Weekly markdown = $10\%$
Calculate price after $1$ week: Step $2$ : Calculate the price after the first week. $\newline$ Price after $1$ week = Initial price $\times$ ( $1$ - markdown percentage) $\newline$ = $\$(80) \times (1 - 0.10)$ $\newline$ = $\$(80) \times 0.90$ $\newline$ = $\$(72)$
Find price after $2$ weeks: Step $3$ : Use the price after the first week to find the price after the second week. $\newline$ Price after $2$ weeks = Price after $1$ week $\times$ $(1 - \text{markdown percentage})$ $\newline$ = $\$(72) \times 0.90$ $\newline$ = $\$(64.80)$
Calculate price after $3$ weeks: Step $4$ : Continue the pattern to calculate the price after the third week. $\newline$ Price after $3$ weeks = Price after $2$ weeks $\times$ ( $1$ - markdown percentage) $\newline$ = $\$(64.80) \times 0.90$ $\newline$ = $\$(58.32)$
Determine price after $10$ weeks: Step $5$ : Apply the same calculation to find the price after $10$ weeks. $\newline$ Price after $10$ weeks = Initial price $\times (0.90)^{10}$ $\newline$ = $\$(80) \times (0.90)^{10}$ $\newline$ = $\$(80) \times 0.3487$ $\newline$ = $\$(27.89)$