Suppose that poaching reduces the population of an endangered animal by 8​% per year. Further suppose that when the population of this animal falls below 70​, its extinction is inevitable​ (owing to the lack of reproductive options without severe​ in-breeding). If the current population of the animal is 1400​, when will it face​ extinction?

Answer:  36 years

Step-by-step explanation:

Here, the current population of the animal is 1400​,

And, the  population of an endangered animal by 8​% per year.

Also, Further suppose that when the population of this animal falls below 70​, its extinction is inevitable​.

Let after x years the population of animal falls below 70,

Therefore,

⇒

⇒

⇒

⇒

⇒x>35.9279739462

Thus, after 36 years( Approx) the population of the animal will be fall towards 70.

Final answer:

The Question involves calculating the time it will take for an endangered animal's population to fall to a level that ensures extinction using the concept of Mathematical Exponential decay. Set up the exponential decay formula, substitute the given values, and solve for time.

Explanation:

The situation described in the question is an example of exponential decay, a concept in mathematics where a quantity decreases at a rate proportional to its current value. In this case, the animal's species population is decreasing by 8​% per year.

To find the time it takes until the endangered animal's population falls below 70 and faces extinction, we need to set up the decay formula:

Where:

P0 is the initial population (1400 in this instance),

r is the rate of decrease (0.08 as 8% in this instance),

P is the predicted population (70 in this instance), and

t is the time in years that we're trying to solve for.

Solving this equation for t, we get:

t = log(P/P0) / log(1 - r)

Substitute the variables with our values, then compute to find the approximate time when the animal's population is expected to fall below 70.

Learn more about Exponential Decay here:

brainly.com/question/2193799

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