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 given by the function V(t) = 20(1.05)^t. What does the number 1.05 represent in this context?
- AThe annual growth rate.
- BThe initial investment amount.
- CThe growth factor per year.
- DThe number of years the investment has grown.
Show answer & explanationAnswer & explanation
Correct answer: C. The growth factor per year.
In an exponential growth function of the form y = a(b)^x, 'b' is the growth factor. Here, 1.05 is the base of the exponent, which represents the factor by which the investment grows each year. This growth factor (1.05) implies a 5% annual growth rate (1.05 = 1 + 0.05).
Why the other options are wrong
- A. The annual growth rate is 0.05 or 5%, which is derived from the growth factor (1.05 - 1 = 0.05). The growth factor itself is not the rate.
- B. The initial investment is represented by 'a', which is 20 (thousand dollars) in this equation.
- D. The number of years is represented by 't', the independent variable in the exponent.
Exponential Growth Function Components
An exponential growth function y = a(b)^x models situations where a quantity increases by a constant percentage over time. 'a' is the initial value, 'b' is the growth factor (1 + rate), and 'x' is the time.
- a = initial amount.
- b = growth factor (b > 1 for growth).
- b = 1 + r, where r is the growth rate as a decimal.
Memory trick: A is start, B is factor, X is time's power.