The population of a town was 5000 in 2010. The population grows at a rate of 1.4% annually. (a) Use the exponential growth model to write an equation that estimates the population t years after 2010.
(b) Estimate the population of the town in 2022. Show your work.

a) P = 5000(1.014)^y

b) 5,908

Step-by-step explanation:

Here, we want to write an exponential growth model;

a)The model will be represented as;

P = 5000( 1.014)^y

where P is the population at a particular year after 2010

y is the number of years after 2010

b.) For 2022;

y = 2022-2010 = 12

P = 5000(1.014)^12

P = 5,908 approximately

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is