Digital SATMath: AlgebraEasy
A biologist observes a population of deer. The population, P(t), after t years can be modeled by the polynomial function P(t) = -t^3 + 12t^2 - 36t + 200. What is the population at t = 0 years?
- A200
- B12
- C0
- D36
Show answer & explanationAnswer & explanation
Correct answer: A. 200
To find the population at t = 0 years, substitute t = 0 into the polynomial function P(t) = -t^3 + 12t^2 - 36t + 200. This gives P(0) = -(0)^3 + 12(0)^2 - 36(0) + 200 = 0 + 0 - 0 + 200 = 200.
Why the other options are wrong
- B. This is a coefficient of t^2, not the population at t=0. Incorrect.
- C. This is an incorrect calculation; substituting t=0 yields 200.
- D. This is a coefficient of t, not the population at t=0. Incorrect.
Evaluating Polynomial Functions
A polynomial function is a function of the form P(x) = a_n x^n + a_{n-1} x^{n-1} + ... + a_1 x + a_0, where 'n' is a non-negative integer and the 'a' values are coefficients. Evaluating it means finding the output value for a given input value of 'x' (or 't').
- Substitute the given value for the variable into every term.
- Follow the order of operations (PEMDAS/BODMAS).
- The constant term (a_0) represents the y-intercept or initial value when x=0.
Memory trick: Plug and play: input goes in, output comes out.