Praxis Core Academic Skills for Educators: Mathematics (5733)Algebra and FunctionsHard
A biologist is tracking the number of cells in a petri dish. The number of cells doubles every 4 hours. If the initial number of cells is 200, which equation models the number of cells N after t hours?
- AN = 200(2)^t
- BN = 200 + 2t
- CN = 200(2)^(t/4)
- DN = 200(2)^(4t)
Show answer & explanationAnswer & explanation
Correct answer: C. N = 200(2)^(t/4)
This is an exponential growth problem where the quantity doubles over a specific period. The general formula for such growth is N = N_0 * (growth factor)^(t / doubling period). Here, the initial number of cells (N_0) is 200, the growth factor is 2 (doubles), and the doubling period is 4 hours.
Why the other options are wrong
- A. This would be correct if the population doubled every 1 hour, not every 4 hours.
- B. This represents linear growth, where the number of cells increases by a constant amount (2) each hour, not by a constant multiple.
- D. This equation implies the population doubles every 1/4 hour, leading to much faster growth.
Exponential Growth (Specific Period)
When a quantity grows by a constant factor over a fixed period (e.g., doubles every X hours), the exponent in the exponential model is the total time divided by that period.
- Formula: N = N_0 * (factor)^(t / period)
- N_0 is the initial amount.
- Factor is the multiplier (e.g., 2 for doubling, 3 for tripling).
- Period is the time it takes for one growth cycle.
Memory trick: Time Over Period is the Exponent Key.