Praxis Core Academic Skills for Educators: Mathematics (5733)Algebra and FunctionsEasy
A biologist is studying a population of insects. The population, P(t), after t days is modeled by the function P(t) = 500 * (1.05)^t. What does the value 1.05 represent in this context?
- AThe number of days it takes for the population to double.
- BThe maximum population the environment can sustain.
- CThe initial population of insects.
- DThe daily growth factor of the insect population.
Show answer & explanationAnswer & explanation
Correct answer: D. The daily growth factor of the insect population.
In an exponential growth model of the form P(t) = P₀ * (1 + r)^t, the base of the exponent (1 + r) represents the growth factor. Here, 1.05 signifies that the population increases by 5% each day.
Why the other options are wrong
- A. This would require a calculation (doubling time) and is not directly represented by 1.05.
- B. This function models unlimited exponential growth and does not include a carrying capacity or maximum population.
- C. This is represented by the P₀ term, which is 500 in this function.
Exponential Growth Factor
In an exponential growth model P(t) = P₀(1+r)^t, the growth factor (1+r) indicates the multiplicative increase per time period.
- It's the base of the exponent.
- If > 1, it represents growth; if < 1, it represents decay.
- It is 1 + the growth rate (as a decimal).
Memory trick: Initial Ants Grow by Rate Times Time.