I need help on my algebra II .A) p(x)= 2,400x+80,000B) p(x)= 80,000(1.03)^xC) p(x)= 80,000(0.03)^xD) p(x)= (1.03)^x

The correct answer is B) y=80000(1.03)ˣ.

Population growth is represented using an exponential equation.  These equations are of the form

y = a(1+r)ˣ, where y is the total population, a is the initial population, r is the growth rate, and x is the amount of time.

We first find the growth rate.  This is the percent of change, which is found by

amount of change/original amount

The amount of change from 2010 to 2011 is 82400-80000=2400.  2400/80000 = 0.03, so r = 0.03.

The growth rate from 2011 to 2012 is (84872-82400)/82400 = 0.03.  Checking the others, they are very close to this as well, so we will use this as r.

Our value of a in the equation is the initial population, 80000.  This gives us:

y = 80000(1+0.03)ˣ = 80000(1.03)ˣ