suppose that in any given year, the population of a certain endangered species is reduce by 25%. if the population is now 7500, in how many years will the population be 4000?

Solve this equation for n, the number of years:

4000 = 7500 * (0.75)^n

4000/7500 = 0.5333 = 0.75^n
n = (log 0.5333)/(log 0.75)

It will take a bit more than 2 years.

To determine the number of years it will take for the population to reach 4000, we need to use the information provided.

Step 1: Calculate the reduction percentage per year.
The population decreases by 25% per year, which means the remaining population after each year is 75% (100% - 25%).

Step 2: Set up the equation.
Let's denote the number of years as "x". Since the population decreases by 25% each year, the equation can be set up as follows:
7500 * (0.75)^x = 4000

Step 3: Solve the equation.
To solve for x, we need to solve the exponential equation. Here's how:
7500 * (0.75)^x = 4000
Divide both sides of the equation by 7500:
(0.75)^x = 4000/7500
Simplify the right side of the equation:
(0.75)^x = 8/15
Next, take the logarithm of both sides using the base 0.75:
log base 0.75 (0.75)^x = log base 0.75 (8/15)
Simplify the left side of the equation:
x = log base 0.75 (8/15)

Step 4: Calculate the value of x.
Using a calculator or math software, evaluate the logarithm to determine the value of x. The result will be the number of years it will take for the population to reach 4000.