GED Mathematical Reasoning TestAlgebraic Problem Solving with Graphs and FunctionsEasy
A client is tracking their savings account balance. The balance (B) in dollars over time (t) in years is represented by the function B(t) = 1500(1.03)^t. What does the value 1500 represent in this context?
- AThe final balance after t years
- BThe number of years the money has been invested
- CThe annual interest rate
- DThe initial amount invested
Show answer & explanationAnswer & explanation
Correct answer: D. The initial amount invested
Exponential growth functions are typically in the form P(t) = P₀(1 + r)^t, where P₀ is the initial amount. In the given function, 1500 occupies the position of P₀, representing the starting balance.
Why the other options are wrong
- A. The final balance is B(t), which depends on 't'.
- B. The number of years is represented by the variable 't', an exponent.
- C. The annual interest rate is derived from the 1.03 factor (3%).
Exponential Growth Function Components
An exponential growth function has the form P(t) = P₀(1 + r)^t, where P(t) is the amount after time t, P₀ is the initial amount, r is the growth rate (as a decimal), and t is the time.
- P₀ is the starting value or initial amount.
- (1 + r) is the growth factor.
- r is the growth rate per time period.
- t is the number of time periods.
Memory trick: P-O-W-E-R means 'P'rincipal 'O'utset 'W'ith 'E'very 'R'ate.