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Chapter 6: Problem 10

You wait for the price to drop on a diamond-studded watch at Macy's. Originally, it cost \(\$ 2500\). The first discount was \(20 \%\) and the second discount is \(50 \%\). a. What are the decay factors for each of the discounts? b. What is the effective decay factor for the two discounts? c. Use the effective decay factor in part b to determine how much you will pay for the watch.

Short Answer

Expert verified
Answer: $1000

Step by step solution

01

Find the decay factors for each discount

To find the decay factor for each discount, we will calculate the percentage remaining after each discount. This can be done by subtracting each discount from 100%. For the first discount of \(20\%\): Decay Factor = \(1 - 0.20 = 0.80\) For the second discount of \(50\%\): Decay Factor = \(1 - 0.50 = 0.50\)
02

Find the effective decay factor for the two discounts

To find the effective decay factor, we multiply the individual decay factors. Effective Decay Factor = \(0.80 \times 0.50 = 0.40\)
03

Calculate the final price of the watch

Now, we apply the effective decay factor calculated in step 2 to the original price of the watch (\(\$ 2500\)) to find the final price after the two consecutive discounts: Final Price = Original Price 脳 Effective Decay Factor Final Price = \( \$ 2500 \times 0.40 = \$ 1000\) So, after the two discounts, you will pay \(\$ 1000\) for the diamond-studded watch at Macy's.

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