Question

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

Answer 1

y = (1/4) 2^x

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.

`\sqrt[4]{x^4}` =
`\sqrt[4]{16}`

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.