* There are 1,000 of an endangered species of bird left. If the population drops by 50% each year, how many years until there are only 1% of the current total left? ( round to a whole number)

1,000 * 0.01 = 10

Year 1 = 500
2 = 250
3 = 125
4 = 62
5 = 31
6 = 16
7 = 8

7 is the correct answer but I feel there needs to be reasoning to it so maybe next time you could give an explanation

To find out how many years until there are only 1% of the current total left, we can set up an equation and solve for the number of years.

Let's start with the current total of the bird population, which is 1,000.
In the first year, the population drops by 50%. Thus, the population will be 1000 - (0.5 * 1000) = 500.

In the second year, the population drops again by 50%. Therefore, the new population will be 500 - (0.5 * 500) = 250.

This pattern continues, so the new population each year can be represented by the equation:
Population = 1000 * (0.5)^n

We want to find the value of n, the number of years, when the population is only 1% of the current total. Mathematically, this can be expressed as:
0.01 * 1000 = 1000 * (0.5)^n

Simplifying the equation:
10 = 0.5^n

To solve for n, we can take the logarithm of both sides of the equation. Using the logarithm base 0.5:
log base 0.5 (10) = n

Using a calculator, we find that the logarithm base 0.5 of 10 is approximately 4.32.

Since the number of years must be a whole number, we can round the value of n to the nearest whole number. Therefore, it will take approximately 4 years until there are only 1% of the current total left.

To find out how many years it will take for the population of the endangered bird species to reach 1% of the current total, we can use exponential decay. Here's how you can calculate it step by step:

1. Start with the current population of the endangered bird species, which is 1,000.
2. Calculate the 50% decrease each year by multiplying the current population by 0.5.
3. Repeat step 2 each year until the population reaches 1% of the current total (which is 1% of 1,000, which is 10).
4. Count the number of years it takes for the population to reach or drop below 10.

Let's follow these steps to find the answer:

Year 1:
Population = 1,000 * 0.5 = 500

Year 2:
Population = 500 * 0.5 = 250

Year 3:
Population = 250 * 0.5 = 125

Year 4:
Population = 125 * 0.5 = 62.5

Year 5:
Population = 62.5 * 0.5 = 31.25

Year 6:
Population = 31.25 * 0.5 = 15.625

Year 7:
Population = 15.625 * 0.5 = 7.8125

Year 8:
Population = 7.8125 * 0.5 = 3.90625

Year 9:
Population = 3.90625 * 0.5 = 1.953125

Year 10:
Population = 1.953125 * 0.5 = 0.9765625 (rounded to 0.976563)

Therefore, it will take 10 years until there are only 1% of the current total left.