At the start, a biologist counts M microbes in a sample. Every day after that, the number of microbes in the sample, is multiplied by some number N.

Question

Write the expression for the number of microbes in the sample
1) after day one 
2) after day two

Use these expressions to help determine the number of microbes in the sample after the eighth day

Using only variables, "m", "n"" and "a", derive the general formula for the number of microbes found after "a" days.

Answer 1

Now we have M
after day 1 , we have Mn
after day 2 , we have Mn(n) = Mn^2
after day 3, we have (Mn^2)(n) = Mn^3
.
.
after day a, we have Mn^a

Number(a) = Mn^a

Answer 2

I don't understand the symbol^.

For example for day 2..Is this the same as saying Mn to the 2nd power?

Answer 3

Ok so I figured out it's exponent...would it be correct to write The answers as follows?

M.n
M.n^2
M.n^8
M.n^a