Answer: 1
Step-by-step explanation: To solve this problem, let's graph the line.
It's important to understand that the y-intercept is the point where the line crosses the y-axis.
So if our line has a y-intercept of 3, it crosses the y-axis up 3 units. So we start this problem by plotting the point (0,3) which I labeled point A.
From there, our slope of -3 can be thought of as -3/1 so we go down 3 units and to the right 1 unit and plot point B. Notice that point B happens to lie on the x-axis at (1,0) and remember that the x-intercept is the point where the line crosses the x-axis. Since our line crosses the x-axis at the point (1,0), it has an x-intercept of 1.
If you're given a y-intercept and a slope like you are in this problem, you won't always be able to determine the x-intercept but things work out nicely here because point B happens to lie on the x-axis.
The equation of the line would be y = -3x + 3
The x intercept is when y is equal to 0.
To solve for the x intercept, plug 0 in for y and then solve
0 = -3x + 3
0-3 = -3x +3 -3
-3 = -3x
-3/-3 = -3/-3x
1 = x
The x intercept is (1,0)
Answer: 186
Step-by-step explanation: the first one is 100 exactly and the second one is 80 for the whole 8 rows and the 6 that are not in the row
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.
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.
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.
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