Question

The current population of a small city is 46500 people. Due to a loss of jobs, the population is decreasing

by an average of 200 people per year. How many years (from now) will it take for the population to
decrease to 42700 people?
A) Write an equation you can use to answer this question. Be sure all the numbers given above appear in
your equation. Use z as your variable and use no commas in your equation.
The equation is
B) Solve your equation in part [A] for 2.
Answer: 2=

Answer 1

19 years

Explanation:

we are looking for the equation of a line that describes this scenario.

we can use the formula

y = mx + b

to solve. since it requests the use of the variable z,

y = mz + b

we know that m = slope. m = change in y/ change in z

y is the population and z is the number of years. for every one year that passes, 200 people leave. m = -200 people/ 1 year

thus the slope is -200

b in the equation is the initial number of people which is 46500

put this all together,

y = -200z + 46500

the time it would take to decrease to 42700

42700 = -200z + 46500

solve for z, z = 19 years