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The value of the angle R in the right triangle PQR is sin⁻¹ 6 / 8
The situation forms a right angle triangle.
<h3>How to find an angle in a right triangle?</h3>The angle R can be found as follows:
using trigonometric ratios,
sin R = opposite / hypotenuse
Therefore,
opposite sides = 6
hypotenuse = 8
sin R = 6 / 8
R = sin⁻¹ 6 / 8
learn more on right triangle here: brainly.com/question/6322314
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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.