Answers are underlined in pink. Hope you can understand my writing! If anything is unclear, just ask!
When you have a negative exponent, you move the base with the negative exponent to the other side of the fraction to make the exponent positive.
For example:
or 
or 

When a base with an exponent is divided by a base with an exponent, you subtract the exponents together. (But you can only combine the exponents when the bases are the same)
For example:
(can't combine because they have different bases of y and x)


When you multiply an exponent directly to a base with an exponent, you multiply the exponents together.
For example:


First multiply the exponents together in the denominator
Now subtract the exponents together
(two negative signs cancel each other out and become positive)


If it has real zeros at x=3 and 7, the factors of f(x) are:
(x-3)(x-7) so f(x) is
f(x)=x^2-10x+21
*5% in decimal form is 0.05.
After one week we have:
N=400*1.05 beetles
After two weeks we have:
N=(400*1.05)*1.05 beetles
After three weeks we have:
N=((400*1.05)*1.05)*1.05 beetles
We can write this as:
Week 1:

Week 2:

Week 3:

From this we can make conclusion that formula for number of beetles after w weeks is given by: