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