In 1997 the population of a small town was 700. If the annual rate of increase is about 0.8%, which value below expresses the population five years later?
A: 5(700)(0.008)
B: 5(700)(1.008)
C: (700)(0.008)^5
D: (700)(1.008)^5
Answers to all questions are appreciated ;)
To find the population five years later, we need to calculate the population after each year and then apply the annual rate of increase.
Let's use the formula A = P(1 + r)^n, where A is the final population, P is the initial population, r is the annual rate of increase as a decimal, and n is the number of years.
Given:
Initial population P = 700
Annual rate of increase r = 0.8% = 0.008
Number of years n = 5
Now let's calculate the options step by step:
Option A: 5(700)(0.008)
This option calculates 5 times the initial population, 700, multiplied by the annual rate of increase, 0.008.
= 5(700)(0.008)
= 280
Option B: 5(700)(1.008)
This option calculates 5 times the initial population, 700, multiplied by the sum of 1 and the annual rate of increase, 0.008.
= 5(700)(1.008)
= 3536
Option C: (700)(0.008)^5
This option calculates the initial population, 700, multiplied by the annual rate of increase, 0.008, raised to the power of 5 (number of years).
= (700)(0.008)^5
= 0.22
Option D: (700)(1.008)^5
This option calculates the initial population, 700, multiplied by the sum of 1 and the annual rate of increase, 0.008, raised to the power of 5 (number of years).
= (700)(1.008)^5
= 778.22
The correct option is D: (700)(1.008)^5, with a result of approximately 778.22.
If you have any further questions, feel free to ask!
To determine the population five years later, we need to calculate the population growth each year and add it to the initial population.
The annual rate of increase is given as 0.8%. Since 0.8% can also be expressed as 0.008 (by dividing by 100), we will use 0.008 as the rate in our calculations.
To find the population after one year, we calculate:
Population after 1 year = Initial population + (Initial population × Rate of increase)
= 700 + (700 × 0.008) = 700 + 5.6 = 705.6
Similarly, for the population after two years:
Population after 2 years = Population after 1 year + (Population after 1 year × Rate of increase)
= 705.6 + (705.6 × 0.008) = 705.6 + 5.648 = 711.248
We continue this process for a total of five years:
Population after 3 years = 711.248 + (711.248 × 0.008) ≈ 717.112
Population after 4 years = 717.112 + (717.112 × 0.008) ≈ 723.242
Population after 5 years = 723.242 + (723.242 × 0.008) ≈ 729.537
So, the population five years later is approximately 729.537.
Now, let's check the given answer choices to find the correct value:
A: 5(700)(0.008) = 28, which is not the correct population growth.
B: 5(700)(1.008) = 3,780, which is much larger than the actual population.
C: (700)(0.008)^5 ≈ 0.0015, which is incorrect.
D: (700)(1.008)^5 ≈ 748.09, which is the closest value to the actual population.
Therefore, the correct expression for the population five years later is (700)(1.008)^5, which is option D.
You only put one
And the rest?
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