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: write functions to represent the number of alligators and crocodiles in the swamp throughout the years. (4 points) part b: how many alligators are in the swamp after 4 years? how many crocodiles are in the swamp after the same number of years? (2 points) part c: after approximately how many years is the number of alligators and crocodiles the same? justify your answer mathematically. (4 points)

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.

the range of a function is the range of y-values for which it is defined, or exists. given that we are only looking at the y-values, we can already discount the first two answers as they deal with the domain of the function (range of x-values).

now, what we need to do is find the smallest and highest y-values for which the function is defined. if you'd like, you could take a ruler and start at the very bottom of the graph, find the lowest point, then move the ruler higher and higher until you reach the highest point. doing so either in your head or with an actual ruler, we can see that the lowest y-value is -5 and the highest y-value is -1.

the question now remains as to whether they are included in the range (fourth answer) or excluded (third answer). the key here is to recognise whether they are marked with an open or a closed circle. since both (-2, -5) and (2, -1) are marked with a closed circle, they are points that exist on the graph and are thus included in the range (note that if they were marked with an open circle like (4, -2) then that would signify that there is a break in the graph at that point).

thus, the fourth answer, (y | -5 ≤ y ≤ -1), is correct.

also note that usually it is good practice to scan your eye inbetween the highest and lowest point for any breaks in the graph - we do have one here at (4, -2), however -2 is still included in the range because there is another point that is included in the graph with the same y-value, ie. point (1, -2).

i hope that but if you require any further explanation don't hesitate to comment below.

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

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