David is observing a bacterial population. The population doubles every 30 minutes. The function p(x)=200*2^x 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.

Answer 1

The y-intercept occurs when x=0, so we can find it by plugging in x=0 into the function:

p(0) = 200*2^0 = 200*1 = 200

Therefore, the y-intercept is 200.

The function p(x)=200*2^x approaches infinity as x approaches infinity, so the graph has an asymptote at y=∞.