Answer:
Step-by-step explanation:
We have given that:
There are 20 alligators in the swamp. Each year, the number of alligators increases by 25%. There are 25 crocodiles in the swamp. Each year, 10 new crocodiles join the swamp
Part A:
According to the above mentioned statement the function for representing the number of alligators and crocodiles in the swap throughout the year is:
Alligators = y=20(1.25)^x (x represents years)
crocodiles: y=10x+25
Part B:
Number of alligators after 4 years in the swap = y=20(1.25)^x
Number of alligators after 4 years in the swap = y=20(1.25)^4
Number of alligators after 4 years in the swap=48.82
This shows that about 48 to 49 alligators will be there in the swap after 4 year
Number of crocodiles after 4 years in the swap = y= 10(4)+25 = 65
Part C:
We will use the graph method to solve this part:
After approximately 7 years, the number of animals of each type will be the same, 95.
1) y-intercept => x = 0, => y = f(0) = 0 - 0 + 0 - 36 = -36
2) x-intercept => y = 0 => factor the function (start by dividing by x -2)
f(x) = (x-2)(x-3)(x-6) =0 => x =2, x = 3, x = 6 (these are the x-intercepts)
3) critical points:
between x = 2 and x = 3, there is a local maximum
between x =3 and x = 6 there is a local minimum
3) Shape.
The function comes growing from - infinity.
In the third quadrant the function is negative (it does not pass throuhg the second quadrant)
It enters to the fourth quadrant intercepting the y-axis at y = -36. It continues growing and intercepts the x-axis at x = 2.
It continues increasing until a maximum local positive value, starts to decrease, intercepts the x-axis at x = 3, continues decreasing, becomes negative, gets a local minimum in the fourth quadrant, starts to increase, intercepts the x-axis at x = 6, becomes positive, and continues growing.
Answer:
Step-by-step explanation:
x y
0 6
24 0
Points are (0,6) and (24,0)
Answer:
x = 3
Step-by-step explanation:
3(x + 2) = 6(x - 1) + 3
Divide both sides by 3.
x + 2 = 2(x - 1) + 1
Distribute the 2 on the right side.
x + 2 = 2x - 2 + 1
Combine like terms on the right side.
x + 2 = 2x - 1
Add 1 to both sides. Subtract x from both sides.
3 = x
x = 3
3/1 is your slope for that
