Digital SATMath: AlgebraEasy
A biologist is studying the growth of a particular type of fungus. The mass of the fungus, M(t), in grams, after t days, is modeled by the equation M(t) = 50 * (1.2)^t. What is the approximate daily percentage growth rate of the fungus?
- A120%
- B80%
- C0.2%
- D20%
Show answer & explanationAnswer & explanation
Correct answer: D. 20%
The exponential growth formula is typically given as P(t) = P_0 * (1 + r)^t, where 'r' is the growth rate. In the given equation, M(t) = 50 * (1.2)^t, the base of the exponent is 1.2. This means 1 + r = 1.2, so r = 0.2. Converting 0.2 to a percentage gives 20%.
Why the other options are wrong
- A. This is the growth factor multiplied by 100%, not the growth rate.
- B. This incorrectly calculates (1 - 0.2) * 100% or (1.2 - 0.4) * 100%.
- C. This is 0.2 as a percentage, which is incorrect as the growth rate is 0.2, not 0.002.
Exponential Growth Rate
The 'r' value in the exponential growth formula P(t) = P_0 * (1 + r)^t, representing the percentage increase per time period.
- Expressed as a decimal in the formula.
- Multiply by 100 to convert to a percentage.
- Represents the rate of change relative to the current amount.
Memory trick: Growth Factor is One Plus Rate.