Question
I received $2,500 for my birthday and opened a savings account. The amount is expected to increase 2% each year. Write a function that models the situation where t represents the number of years. How much money will I have in 3 years?(3 points)
f(x)= ()t
In 3 years the account will have $.
f(x)= ()t
In 3 years the account will have $.
Answers
GPT-4o mini
To model the situation where your savings increase by 2% each year, you can use the following function:
\[
f(t) = P(1 + r)^t
\]
Where:
- \( P = 2500 \) (the initial amount)
- \( r = 0.02 \) (the interest rate, 2%)
- \( t \) is the number of years
So, the function that models your savings over time is:
\[
f(t) = 2500(1 + 0.02)^t
\]
To find out how much money you will have in 3 years, we can substitute \( t = 3 \) into the function:
\[
f(3) = 2500(1 + 0.02)^3
\]
\[
f(3) = 2500(1.02)^3
\]
\[
f(3) = 2500(1.061208)
\]
\[
f(3) \approx 2500 \times 1.061208 \approx 2652.52
\]
In 3 years, the account will have approximately **$2,652.52**.
\[
f(t) = P(1 + r)^t
\]
Where:
- \( P = 2500 \) (the initial amount)
- \( r = 0.02 \) (the interest rate, 2%)
- \( t \) is the number of years
So, the function that models your savings over time is:
\[
f(t) = 2500(1 + 0.02)^t
\]
To find out how much money you will have in 3 years, we can substitute \( t = 3 \) into the function:
\[
f(3) = 2500(1 + 0.02)^3
\]
\[
f(3) = 2500(1.02)^3
\]
\[
f(3) = 2500(1.061208)
\]
\[
f(3) \approx 2500 \times 1.061208 \approx 2652.52
\]
In 3 years, the account will have approximately **$2,652.52**.