Praxis Core Academic Skills for Educators: Mathematics (5733)Algebra and FunctionsMedium
A financial analyst is modeling the growth of an investment. The value of the investment, V(t), after t years is given by the function V(t) = 5000(1.04)^t. What is the annual percentage growth rate of this investment?
- A40%
- B0.04%
- C4%
- D1.04%
Show answer & explanationAnswer & explanation
Correct answer: C. 4%
In an exponential growth function of the form P(t) = P_0(1 + r)^t, 'r' represents the growth rate as a decimal. Here, 1 + r = 1.04, so r = 0.04. To convert this to a percentage, multiply by 100.
Why the other options are wrong
- A. Incorrect. This would imply a growth factor of 1.40.
- B. Incorrect. This would be 0.0004 as a decimal.
- D. Incorrect. This is the growth factor, not the percentage rate.
Exponential Growth Rate
The rate at which a quantity increases over time, expressed as a percentage or decimal in an exponential growth model.
- Model: P(t) = P_0(1 + r)^t
- 'r' is the growth rate as a decimal.
- Convert 'r' to a percentage by multiplying by 100.
Memory trick: Remember, the 'r' in (1+r) is the decimal rate, just like 'interest rate' is often a percentage.