David is observing a bacterial population. The population doubles every 30 minutes. The function p(x)=200x*2^2 models the population, where x is the number of 30-minute periods since David began observing.

Question

Identify the y-intercept and the asymptote of the graph of the function.
a
y-intercept = 200; asymptote: x = 0
b
y-intercept = 0; asymptote: y = 0
c
y-intercept = 0; asymptote: x = 0
d
y-intercept = 200; asymptote: y = 0

Answer 1

The correct answer is a) y-intercept = 200; asymptote: x = 0.

The y-intercept occurs when x = 0, so plugging in x = 0 into the function we get p(0) = 200(0)*2^2 = 0. Therefore, the y-intercept is at y = 0.

The asymptote occurs when the population approaches infinity as x approaches infinity, but in this case the population doubles every 30 minutes so it will never actually reach infinity. However, as x approaches infinity, the population will continue to grow exponentially. Thus, the asymptote is x = 0.