GED Mathematical Reasoning TestAlgebraic Problem Solving with Graphs and FunctionsMedium
A client is managing their financial portfolio. The value of their investment, V(t), in thousands of dollars, after t years, is represented by the function V(t) = 50 * (1.07)^t. What does the value '1.07' represent in this function?
- AThe growth factor per year.
- BThe number of years the investment has been held.
- CThe initial investment amount.
- DThe annual growth rate.
Show answer & explanationAnswer & explanation
Correct answer: A. The growth factor per year.
In an exponential growth function of the form V(t) = A_0 * b^t, A_0 is the initial amount and 'b' is the growth factor. The growth factor (b) is equal to (1 + rate of growth). Here, b = 1.07, meaning the investment grows by 7% (0.07) each year, so 1.07 is the factor by which the investment is multiplied each year.
Why the other options are wrong
- B. The number of years is represented by 't', the exponent.
- C. The initial investment amount is 50 (thousands of dollars).
- D. The annual growth rate is 0.07 or 7%, not 1.07. The growth factor is 1 + rate.
Exponential Growth Function Components
In A(t) = A_0 * b^t, A_0 is the initial amount, 'b' is the growth factor (1 + growth rate), and 't' is time.
- A_0 = initial amount
- b = growth factor (multiplier per period)
- b = 1 + r (where r is the growth rate as a decimal)
- t = number of periods
Memory trick: Start with A_0, Grow by B, Time is T!