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 the amount in the savings account increases by 2% each year, you can use an exponential growth function. The function can be represented as:
\[ f(t) = P(1 + r)^t \]
where:
- \( P \) is the initial amount (in this case, $2,500),
- \( r \) is the growth rate (2% or 0.02),
- \( t \) is the number of years.
Thus, the function for your situation would be:
\[ f(t) = 2500(1 + 0.02)^t \]
or simplified:
\[ f(t) = 2500(1.02)^t \]
To find out how much money you will have in 3 years, substitute \( t = 3 \) into the function:
\[ f(3) = 2500(1.02)^3 \]
Now, calculating \( (1.02)^3 \):
\[
1.02^3 \approx 1.061208
\]
Now substitute it back into the equation:
\[
f(3) = 2500 \times 1.061208 \approx 2653.02
\]
So in 3 years, the account will have approximately $2,653.02.
In summary, the function is:
\[ f(t) = 2500(1.02)^t \]
And in 3 years, the account will have approximately:
\[ \$2653.02 \]
\[ f(t) = P(1 + r)^t \]
where:
- \( P \) is the initial amount (in this case, $2,500),
- \( r \) is the growth rate (2% or 0.02),
- \( t \) is the number of years.
Thus, the function for your situation would be:
\[ f(t) = 2500(1 + 0.02)^t \]
or simplified:
\[ f(t) = 2500(1.02)^t \]
To find out how much money you will have in 3 years, substitute \( t = 3 \) into the function:
\[ f(3) = 2500(1.02)^3 \]
Now, calculating \( (1.02)^3 \):
\[
1.02^3 \approx 1.061208
\]
Now substitute it back into the equation:
\[
f(3) = 2500 \times 1.061208 \approx 2653.02
\]
So in 3 years, the account will have approximately $2,653.02.
In summary, the function is:
\[ f(t) = 2500(1.02)^t \]
And in 3 years, the account will have approximately:
\[ \$2653.02 \]