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.
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.
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
I don't understand the symbol^.
For example for day 2..Is this the same as saying Mn to the 2nd power?
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
1) The expression for the number of microbes in the sample after day one can be written as M * N since the number of microbes, M, is multiplied by N.
2) After day two, the expression for the number of microbes in the sample becomes (M * N) * N = M * N^2. This is because after the first day, the number of microbes is M * N, and on the second day, this count is multiplied by N again.
To determine the number of microbes in the sample after the eighth day, we can use the expression for day two and keep multiplying by N for each subsequent day. Since N is constant, we can raise it to the power of the number of days. Therefore, the expression becomes M * N^8.
To derive the general formula for the number of microbes after "a" days, we can follow the same logic. After the first day, the count is M * N. On the second day, it becomes M * N^2. Continuing this pattern, after "a" days, the expression becomes M * N^a. This is because the count is multiplied by N for each day, and after "a" days, N is raised to the power of "a".