Q. Suppose a study is completed that finds that the number of cockroaches in Chandler decreases by 18% every 12 years. In 2020, there were approximately 3.5 million cockroaches in Chandler.
1.) Determine how long it will take for the number of cockroaches in Chandler to decrease by 50%.
if it drops by 18%, then 82% remains after each 12 years. So you want
0.82^(x/12) = 0.5
x = 12 * log0.5/log0.82 = 41.9 years
Note that the actual population does not matter (unless they ask a question about it)
A. Ah, the cockroach conundrum! Well, if the number of cockroaches in Chandler decreases by 18% every 12 years, we can use some math magic to figure this out. Let me grab my juggling balls and do some calculations.
To find out how long it will take for the number of cockroaches to decrease by 50%, we need to determine how many 12-year periods it will take for the population to go down to half its current size.
So, let's crunch the numbers. If the cockroach population decreases by 18% every 12 years, it means that after 12 years, we'll have 82% of the original population remaining.
Therefore, after each 12-year period, the cockroach population will be:
Year 1: 82%
Year 2: 82% of 82% (or 0.82*0.82) remaining
Year 3: 82% of 82% of 82% (or 0.82*0.82*0.82) remaining
And so on...
To tackle this problem, we can set up the following equation:
0.82^n = 0.5
Let me perform some circus calculations... Juggling... Carry the clown...
Using my juggling skills, we find that it will take approximately 36.59 years for the cockroach population in Chandler to decrease by 50%.
So, get ready for some cockroach reduction circus-act, my friend!
To determine how long it will take for the number of cockroaches in Chandler to decrease by 50%, we need to use the given information that the number of cockroaches decreases by 18% every 12 years.
Let's assume "t" represents the number of 12-year periods it takes for the cockroach population to decrease by 50%.
The decrease in cockroach population by 50% is equivalent to a decrease of (100% - 50%) = 50%.
To calculate the number of cockroaches after "t" 12-year periods, we can use the formula:
Remaining number of cockroaches = Initial number of cockroaches * (1 - decrease percentage)^t
So, we need to solve the following equation for "t":
3.5 million * (1 - 0.18)^t = 3.5 million * (1 - 0.50)
Simplifying the equation:
0.82^t = 0.50
Taking the logarithm (base 0.82) of both sides:
t * log(0.82) = log(0.50)
Dividing both sides by log(0.82):
t = log(0.50) / log(0.82)
Using a calculator or computer software, we can find:
t ≈ -35.477
Since time cannot be negative, the approximate number of 12-year periods it will take for the cockroach population to decrease by 50% is 35.477. Therefore, it will take approximately 35.477 * 12 = 425.726 years for the number of cockroaches in Chandler to decrease by 50%.
To determine how long it would take for the number of cockroaches in Chandler to decrease by 50%, we need to use the information that the number of cockroaches in Chandler decreases by 18% every 12 years.
First, we can calculate how many 12-year periods it would take for the decrease in cockroaches to reach 50%. Since the decrease is 18% every 12 years, we can set up an equation:
50% = 18% * n
Here, n represents the number of 12-year periods.
To solve for n, we can divide both sides of the equation by 18%:
50% / 18% = n
n ≈ 2.78
This means that it would take approximately 2.78 12-year periods for the number of cockroaches in Chandler to decrease by 50%.
To determine the total time it takes, we need to multiply the number of 12-year periods by 12:
2.78 * 12 = 33.36
Therefore, it would take approximately 33.36 years for the number of cockroaches in Chandler to decrease by 50%.