Question
Your starting salary at a new company is $34,000 and it increase by 2.5% each year.Write an exponential growth function to represent this situation.
Group of answer choices
O y = 34 * (1.025) ^ t
y = 34000 * (1.025) ^ t
O y = 3400 * (125) ^ t
O y = 340 * (1.25) ^ t
Group of answer choices
O y = 34 * (1.025) ^ t
y = 34000 * (1.025) ^ t
O y = 3400 * (125) ^ t
O y = 340 * (1.25) ^ t
Answers
GPT-4o mini
To represent the situation of a starting salary of $34,000 that increases by 2.5% each year, we can use the exponential growth function in the form:
\[ y = P(1 + r)^t \]
where:
- \( P \) is the initial amount (in this case, the starting salary),
- \( r \) is the growth rate (in decimal form), and
- \( t \) is the number of years.
In your scenario:
- \( P = 34,000 \)
- \( r = 0.025 \) (2.5% expressed as a decimal)
Plugging these values into the formula, we get:
\[ y = 34000(1 + 0.025)^t \]
\[ y = 34000(1.025)^t \]
Therefore, the correct exponential growth function is:
**y = 34000 * (1.025) ^ t**
So, the correct answer from the choices provided is:
**y = 34000 * (1.025) ^ t**
\[ y = P(1 + r)^t \]
where:
- \( P \) is the initial amount (in this case, the starting salary),
- \( r \) is the growth rate (in decimal form), and
- \( t \) is the number of years.
In your scenario:
- \( P = 34,000 \)
- \( r = 0.025 \) (2.5% expressed as a decimal)
Plugging these values into the formula, we get:
\[ y = 34000(1 + 0.025)^t \]
\[ y = 34000(1.025)^t \]
Therefore, the correct exponential growth function is:
**y = 34000 * (1.025) ^ t**
So, the correct answer from the choices provided is:
**y = 34000 * (1.025) ^ t**