Digital SATMath: Advanced MathEasy
A scientist is observing the growth of a bacterial colony. The number of bacteria, P(t), after t hours is modeled by the function P(t) = 500 * 2^(t/3). What is the initial number of bacteria in the colony?
- A1500
- B0
- C167
- D500
Show answer & explanationAnswer & explanation
Correct answer: D. 500
The initial number of bacteria corresponds to the value of P(t) when t=0. Substituting t=0 into the function gives P(0) = 500 * 2^(0/3) = 500 * 2^0 = 500 * 1 = 500.
Why the other options are wrong
- A. This might result from incorrectly multiplying 500 by something other than 1 when t=0.
- B. This would mean no bacteria were present to begin with, which is incorrect for a growing colony.
- C. This is approximately 500/3, which might be a misinterpretation of the exponent.
Initial Value in Exponential Functions
For an exponential function in the form f(x) = a * b^x, the initial value (when x=0) is 'a'.
- The 'a' term represents the starting quantity.
- Any non-zero number raised to the power of 0 is 1.
- The initial value is found by setting the independent variable to zero.
Memory trick: Start with 'A' for 'Amount at first' in 'A times B to the X'.