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PLEASE HELP ME WITH 9 (and 7a./7b. If you can) :)

y = (1/4) 2^x

Step-by-step explanation:

Remark

y = a * x^n is the general equation. Let's see what that means.

Solution

Solve for x

t_12 = a x^12

1024 = a x^12

t_8 = a x^8

64 = a x^8

Now divide the two equations.

1024/64 = a x^12/a x^8       Cancel out the as

1024 / 64 = x^12 / x^8

16 = x^(12 - 8)

16 = x^4                               Take the 4th root of both sides.

 =  

x = 2

Go back and solve for a

y_12 = a x^12

1024 = a 2^12

1024 = a 4096                   Divide by 4096

1024 / 4096 = a

a = 1/4

Problem 7

a) First of negative numbers are probably not a good idea. It means that the population is going to decrease. That's not what will happen if you take care of the fruit flies.

So for the domain, 0 is a good starting point.

That will give you 100 flies on day 0. That's how many you bought.

I'm not a biologist so I have no idea in the world how long a fruit fly will live even with the best of care. I'm going to try 60 days and see what happens.

y = 100 * 1.05 ^60

y = 100 * 18.68

y = 1868

Is this number reasonable? Even with the biggest olive jar you can find, and the best care, I don't think that number is realistic. It's too large. Eventually all will die of disease because they are living in their own waste. So Let's try 20 days

y = 100 * 1.05^20

y = 100 * 2.65

y = 265

That's a lot more reasonable. So for convenience sake let us say that 265 flies could live for 20 days

So to answer the question

The domain would be 0 to 20

The range would be 100 to 265

b)

2 weeks = 2*7 days

2 weeks = 14 days

y = 100 * 1.05^14

y = 100 * 1.98

y = 198 fruit flies.

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.

question 1 is 8, question 2 is 9, question 3 is 24

step-by-step explanation:

now, the numbers they give you at the top are the key. from there, you just have to plug and chug! let's try 1, 2, and 3!

key: a=3, b=5, c=6

1. a+5

remember, a=3, so we plug that in to get 3+5=8

2. 15-c

c=6, so we plug that in to get 15-6=9

3. 4b

b=6, so we plug it in to get 4*6=24

time to try the rest on your own! if you put the answers below in a comment, i'll check them for you!