Question

The first time a census was taken in Michele Corners, the population was 1772. Each year after that, the population was about 9% higher than it was the previous year.
Sketch the graph that represents the situation. Let x represent the number of years since the first census was taken.

What are the coordinates of the point that contains the ­y-intercept?

Answer 1

We are given

The first time a census was taken in Michele Corners, the population was 1772

so, initial population =1772

so, $P=1772$

Each year after that, the population was about 9% higher than it was the previous year

so, r=9%

$r=0.09$

now, we can use formula

$y=P(1+r)^{x}$

y is population after x years

x represent the number of years since the first census was taken

so, we get equation as

$y=1772(1+0.09)^{x}$

$y=1772(1.09)^{x}$

y-intercept:

so, we can plug x=0 to get y-intercept

$y=1772(1.09)^{0}$

$y=1772$...........Answer