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 you have an initial amount of $2,500 that increases by 2% each year, you can use the formula for exponential growth:

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

Where:
- \( P \) is the initial principal balance ($2,500)
- \( r \) is the rate of increase (2% or 0.02)
- \( t \) is the number of years

Substituting the values into the formula gives us:

\[
f(t) = 2500(1 + 0.02)^t
\]
\[
f(t) = 2500(1.02)^t
\]

Now, to find out how much money you will have in 3 years, substitute \( t = 3 \) into the function:

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

Calculating this, we first compute \( (1.02)^3 \):

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

Now, multiply this by $2,500:

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

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

To summarize:

- The function modeling the situation is:
\[
f(t) = 2500(1.02)^t
\]

- In 3 years, the account will have approximately:
\[
\$2,653.02
\]

In final blanks:

1. \( f(x) = 2500(1.02)^t \)
2. In 3 years the account will have \$2,653.02.