Praxis Core Academic Skills for Educators: Mathematics (5733)Algebra and FunctionsEasy
A biologist is studying a population of fruit flies. The population P(t) after t days is modeled by the function P(t) = 50 * (1.15)^t. What was the initial population of fruit flies?
- A1.15
- B50
- C15
- D57.5
Show answer & explanationAnswer & explanation
Correct answer: B. 50
In an exponential growth model of the form P(t) = P_0 * (1 + r)^t, P_0 represents the initial amount when t = 0. In this equation, 50 is the initial population.
Why the other options are wrong
- A. This is the growth factor, not the initial population.
- C. This is related to the percentage growth rate (15%), not the initial population.
- D. This would be the population after 1 day, not the initial population.
Initial Value of Exponential Function
For an exponential function y = a * b^x, the 'a' term represents the initial value or the value of y when x = 0.
- It's the y-intercept of the exponential curve.
- Represents the starting quantity or amount.
- Found by setting the independent variable to zero.
Memory trick: Start with A, grow by B, over X time.