ACT (Enhanced)MathematicsMedium
A financial analyst is modeling the growth of an investment. The value of the investment, V, in dollars, after t years, is given by V(t) = 5000(1.06)^t. What is the annual percentage growth rate of this investment?
- A0.06%
- B6.0%
- C5.0%
- D106.0%
Show answer & explanationAnswer & explanation
Correct answer: B. 6.0%
In an exponential growth model V(t) = P(1+r)^t, the base of the exponent (1+r) represents the growth factor. To find the percentage growth rate, subtract 1 from the growth factor and multiply by 100.
Why the other options are wrong
- A. This is the growth rate as a decimal, but with an incorrect percentage conversion.
- C. This is an arbitrary value and does not correspond to the growth factor.
- D. This incorrectly includes the base of 1, resulting in an overly large percentage.
Exponential Growth Rate
The rate at which a quantity increases over time, expressed as a percentage, in an exponential growth model.
- Model form: A(t) = P(1 + r)^t, where r is the growth rate.
- To find percentage, convert decimal 'r' to percent (r * 100%).
- The base of the exponent (1+r) is the growth factor.
Memory trick: Growth factor's 'r' is key, convert to percent, you'll see!