Digital SATMath: AlgebraEasy
A biologist is observing the growth of a bacterial colony. The colony's population, P(t), in thousands, after t hours, can be modeled by the function P(t) = 5 * 2^(t/3). What is the population of the colony after 9 hours?
- A160 thousand
- B40 thousand
- C80 thousand
- D120 thousand
Show answer & explanationAnswer & explanation
Correct answer: B. 40 thousand
To find the population after 9 hours, substitute t=9 into the given exponential function and calculate the result. P(9) = 5 * 2^(9/3) = 5 * 2^3 = 5 * 8 = 40.
Why the other options are wrong
- A. This would be 5 * 2^5, not 5 * 2^3.
- C. This would be 5 * 2^4, not 5 * 2^3.
- D. This is an incorrect calculation, possibly multiplying 5 by 2 and then cubing.
Evaluating Exponential Functions
Substituting a given value into an exponential function to determine the corresponding output.
- Exponential functions have the form f(x) = a * b^x or f(x) = a * b^(x/c).
- The base 'b' represents the growth or decay factor.
- Careful with order of operations (exponents before multiplication).
Memory trick: Plug in 't', then 'Power up' the base, finally Multiply.