Ed's new car has a value of $23,500, but it is expected to depreciate at a rate of 7.5% per year. If you were to write an exponential decay function to represent this situation, what would the initial value be? O 23,500 O 107.5 O 92.5 O 7.5
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
 alt="**Understanding Exponential Decay in Car Depreciation**
Ed's new car has a value of $23,500, but it is expected to depreciate at a rate of 7.5% per year. If you were to write an exponential decay function to represent this situation, what would the initial value be?
**Multiple Choice Options:**
- ○ 23,500
- ○ 107.5
- ○ 92.5
- ○ 7.5
Explanation:
In the context of exponential decay, the initial value in this scenario refers to the starting value of Ed’s car before any depreciation occurs.
### Understanding the Initial Value:
When dealing with exponential decay, which can be represented by the formula \( V(t) = V_0 \times (1 - r)^t \), where:
- \( V(t) \) is the value of the car at time \( t \).
- \( V_0 \) is the initial value (the value of the car when \( t = 0 \)).
- \( r \) is the rate of depreciation.
- \( t \) is the time in years.
Here, the initial value \( V_0 \) is simply the original purchase price of the car, which is $23,500.
Hence, the correct answer is:
- ○ 23,500
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