Question

A student buys a new laptop for $\$ 1500$ when she arrives as a freshman. A year later, the computer is worth approximately $\$ 750 .$ If the depreciation continues at the same rate, how much would she expect to sell her laptop for when she graduates 4 years after she bought it?

Name: Problem 56, Chapter 3: Precalculus
Uploaded: 2020-08-09T21:30:04-08:00
Duration: 38 s
Channel: Katelyn Chen
Description: A student buys a new laptop for 1500 when she arrives as a freshman. A year later, the computer is worth approximately 750 . If the depreciation continues at the same rate, how much would she expect to sell her laptop for when she graduates 4 years after she bought it?

   A student buys a new laptop for $\$ 1500$ when she arrives as a freshman. A year later, the computer is worth approximately $\$ 750 .$ If the depreciation continues at the same rate, how much would she expect to sell her laptop for when she graduates 4 years after she bought it?

Precalculus

Cynthia Young 2nd Edition

Chapter 3, Problem 56

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Solved by Expert Katelyn Chen

08/09/2020

Step 1

The laptop's value decreases by half each year. This is a geometric sequence where the common ratio is 0.5 (50% of the previous year's value). Show more…

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A student buys a new laptop for $\$ 1500$ when she arrives as a freshman. A year later, the computer is worth approximately $\$ 750 .$ If the depreciation continues at the same rate, how much would she expect to sell her laptop for when she graduates 4 years after she bought it?

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Key Concepts

Exponential Decay

Exponential decay is a mathematical concept describing the process where a quantity reduces by a constant factor over equal intervals of time. In finance and depreciation, it models scenarios where an asset loses a consistent proportion of its value each period, leading to a rapid decrease initially that slows over time.

Depreciation

Depreciation refers to the process by which an asset loses its value over time due to usage, wear and tear, obsolescence, or market conditions. It is a key concept in accounting and financial management for understanding how the worth of tangible assets diminishes.

Constant Rate Depreciation

Constant rate depreciation is a method where an asset’s value decreases by a fixed percentage over each time period. This approach simplifies calculations as the decline in value follows a consistent pattern, allowing for straightforward prediction of future asset value.

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