twenty-five multiplied by three.
Complete question :
In one year, the population of Douglas, the former copper mining town on the U.S.-Mexico border, shrunk by 200. Over the last ten years, the town’s population is going down at an average rate of 1.16% per year. Douglas’ current population in November 2020 is 15,140. a. Write an equation to model the population decay of Douglas using the data given. b. If the town’s population loss continues to occur at this rate, what will the population of Douglas in 6 months from now? Round your answer to the nearest integer. c. If the town’s population loss continues to occur at this rate, what will the population of Douglas in one year? Round your answer to the nearest integer. d. If the town’s population loss continues to occur at this rate, what will the population of Douglas in November 2027? Round your answer to the nearest integer.
Answer:
15052 ; 14,964 ; 13953
Step-by-step explanation:
Given that:
Rate of population decline = 1.16% annually
Population in November 2020 = 15140
A = I(1 - r)^t
Where ;
A = final population
I = initial population
r = rate of decline
t = number of years
Population in 6 months
t = 6 months = 0.5 year, r = 1.16% = 0.0116
A = 15140(1 - 0.0116)^0.5
A = 15140(0.9884)^0.5
A = 15051.931
A = 15052 ( nearest integer)
Population after 1 year :
A = 15140(1 - 0.0116)^1
A = 15140(0.9884)^1
A = 14964.376
A = 14964 ( nearest integer)
Population in 2027:
t = 2027 - 2020
A = 15140(1 - 0.0116)^7
A = 15140(0.9884)^7
A = 13952.596
A = 13953 ( nearest integer)
We need to find m and b to find in the equation of a line:
y = mx + b
↑ <span>↑
slope y-intercept
To find m, the slope, we need to find the rise over the run of the line. You pick two points and use the y values finding the difference of them and do the same for the x values and put them on the bottom. Let's use the points (0, -2) and (4, 0):
</span>↑ ↑<span>
(x₁, y₁) (x₂, y₂)
m = (y</span>₂ - y₁)/(x₂ - x₁)
m = (-2 - 0)/(0 - 4)
m = (-2)/(-4)
m = 1/2
The slope is positive since the line is going upward from left to right.
Now we need b, the y intercept, where the line intersects with the y axis, simply by looking at the graph. b is -2.
Thus, the answer is C. y = 1/2x - 2.
Let be "n" the number mentioned in the exercise.
You need to remember that:
1. In Math word problems:
- The word "times" means multiplication.
- The word "twice" indicates that something is multiplied by 2.
- "Sum" is the result of an Addition.
2. In inequalities, "Less than" is represented with the following symbol:
Then, based on the above, you know that "3 times a number" can be expressed as:
And "Twice the same number":
Therefore, "The sum of 3 times a number and twice the same number is less than 45" can be represented with the following inequality:
The answer is: Option a.