Answer:
38.26 years.
Step-by-step explanation:
We have been given that the population of an endangered animal by reduces 8% per year. the current population of the animal is 1700. When the population of this animal falls below 70, its extinction is inevitable.
Let us write the model for population of this animal (y) after x years.
Since we know that an exponential decay function is in form: , where,
a= Initial value.
r = Rate in decimal form.
Let us convert our given rate in decimal form.
Upon substituting a= 1700 and r = 0.08 in exponential function, we will get the model of animal population as:
Let us find, when the animal population will face extinction by substituting y=70 in our function.
Let us take natural log of both sides of our equation.
Therefore, the population of the animal will face extinction after 38.26 years.