Question
You bought $2000 worth of stocks in 2012. The value of the stocks has been decreasing by 10% each year. Write an exponential decay function to represent this situation.
Group of answer choices
y = 2000 * (0.9) ^ t
y = 200 * (0.99) ^ t
y = 20 * (0.9) ^ t
y = 2000 * (0.009) ^ t
Group of answer choices
y = 2000 * (0.9) ^ t
y = 200 * (0.99) ^ t
y = 20 * (0.9) ^ t
y = 2000 * (0.009) ^ t
Answers
GPT-4o mini
To model the situation where the value of the stocks is decreasing by 10% each year, we can use an exponential decay function. The general form of the function is:
\[ y = y_0 \cdot (1 - r)^t \]
where:
- \( y_0 \) is the initial amount (in this case, $2000),
- \( r \) is the rate of decay (10%, or 0.10),
- \( t \) is the time in years.
Since the stocks are decreasing by 10% each year, the value at time \( t \) can be represented as:
\[ y = 2000 \cdot (1 - 0.10)^t \]
\[ y = 2000 \cdot (0.90)^t \]
Therefore, the correct exponential decay function is:
**y = 2000 * (0.9) ^ t**
So the matching choice is:
**y = 2000 * (0.9) ^ t**
\[ y = y_0 \cdot (1 - r)^t \]
where:
- \( y_0 \) is the initial amount (in this case, $2000),
- \( r \) is the rate of decay (10%, or 0.10),
- \( t \) is the time in years.
Since the stocks are decreasing by 10% each year, the value at time \( t \) can be represented as:
\[ y = 2000 \cdot (1 - 0.10)^t \]
\[ y = 2000 \cdot (0.90)^t \]
Therefore, the correct exponential decay function is:
**y = 2000 * (0.9) ^ t**
So the matching choice is:
**y = 2000 * (0.9) ^ t**