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 * (1.05)^t. What is the initial population of fruit flies?
- A52.5
- B50
- C1.05
- D105
Show answer & explanationAnswer & explanation
Correct answer: B. 50
In an exponential growth function of the form y = a(b)^x, 'a' represents the initial value or the value of y when x (or t) is 0. Here, 'a' is 50.
Why the other options are wrong
- A. This is the population after 1 day (50 * 1.05 = 52.5), not the initial population.
- C. This is the growth factor, indicating a 5% daily increase, not the initial population.
- D. This might be a misinterpretation or calculation, perhaps 50 * 2 + 5.
Initial Value of Exponential Function
The initial value of an exponential function y = a(b)^x is the value of 'a', representing the quantity when the independent variable x (often time) is zero.
- It is the y-intercept of the graph.
- Represents the starting amount or population.
- Found by setting x=0: y = a(b)^0 = a(1) = a.
Memory trick: 'A' is for 'At the start'.