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 $.

Answer 1

To model the situation where the initial amount of money is $2,500 and it increases at a rate of 2% each year, we can use an exponential growth function. The general formula for exponential growth can be represented as:

\[ f(t) = P(1 + r)^t \]

where:
- \( P \) is the principal amount (initial investment),
- \( r \) is the annual interest rate (as a decimal),
- \( t \) is the time in years.

In your case:
- \( P = 2500 \)
- \( r = 0.02 \) (which is 2% expressed as a decimal)

So we can write the function as:

\[ f(t) = 2500(1 + 0.02)^t \]

This simplifies to:

\[ f(t) = 2500(1.02)^t \]

To find out how much money you will have in 3 years, substitute \( t = 3 \):

\[ f(3) = 2500(1.02)^3 \]

Now we need to calculate \( (1.02)^3 \):

\[
(1.02)^3 \approx 1.061208
\]

Now, multiply this result by 2,500:

\[
f(3) = 2500 \times 1.061208 \approx 2653.02
\]

So, in 3 years, the account will have approximately **$2,653.02**.

Therefore, the final answer is:
In 3 years the account will have **$2,653.02**.