Question
In 2010 an item cost $9.00. The price increase by 1.5% each year. Write an exponential growth function to represent this situation.
Group of answer choices
y = 9 * (1.015) ^ t
y = 9(1.025)
y = 99 * (1.425) ^ t
y = 99(1.025)
Group of answer choices
y = 9 * (1.015) ^ t
y = 9(1.025)
y = 99 * (1.425) ^ t
y = 99(1.025)
Answers
GPT-4o mini
To model the given situation of an item costing $9.00 in 2010 with a price increase of 1.5% each year, we can use the formula for exponential growth:
\[ y = y_0 \cdot (1 + r)^t \]
where:
- \( y_0 \) is the initial amount (which is $9.00),
- \( r \) is the growth rate (1.5% expressed as a decimal is 0.015),
- \( t \) is the time in years since 2010.
Substituting these values into the formula:
\[ y = 9 \cdot (1 + 0.015)^t \]
\[ y = 9 \cdot (1.015)^t \]
Thus, the correct exponential growth function that represents this situation is:
\[ y = 9 \cdot (1.015)^t \]
Therefore, the answer from the choices you provided is:
**y = 9 * (1.015) ^ t**
\[ y = y_0 \cdot (1 + r)^t \]
where:
- \( y_0 \) is the initial amount (which is $9.00),
- \( r \) is the growth rate (1.5% expressed as a decimal is 0.015),
- \( t \) is the time in years since 2010.
Substituting these values into the formula:
\[ y = 9 \cdot (1 + 0.015)^t \]
\[ y = 9 \cdot (1.015)^t \]
Thus, the correct exponential growth function that represents this situation is:
\[ y = 9 \cdot (1.015)^t \]
Therefore, the answer from the choices you provided is:
**y = 9 * (1.015) ^ t**