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, over t years, is modeled by the function V(t) = 15(1.06)^t. What does the number 1.06 represent in this function?
- AThe total investment after 1 year
- BThe number of years until the investment doubles
- CThe initial investment of $1.06 thousand
- DA 6% annual increase in value
Show answer & explanationAnswer & explanation
Correct answer: D. A 6% annual increase in value
In an exponential growth function of the form y = a(b)^x, 'a' is the initial value and 'b' is the growth factor. The growth factor is calculated as (1 + rate of growth). Here, b = 1.06, so 1 + rate = 1.06, which means the rate is 0.06 or 6%.
Why the other options are wrong
- A. The total investment after 1 year would be 15 * (1.06)^1 = 15.9 thousand dollars, not just 1.06.
- B. The doubling time would require solving 2 = (1.06)^t, which is not what 1.06 represents directly.
- C. The initial investment is represented by 'a', which is 15 (thousand dollars).
Exponential Growth Function Components
An exponential growth function, typically y = a(b)^x or y = a(1+r)^x, models situations where a quantity increases by a fixed percentage over equal time intervals.
- 'a' is the initial amount or starting value.
- 'b' (or 1+r) is the growth factor, where 'r' is the growth rate as a decimal.
- 'x' (or t) is the number of time periods.
- The growth factor is always greater than 1.
Memory trick: Growth Factor is '1 + Rate' – 'R' for 'Rise' in value!