Question

Logarithms:

The number of cells in an embryo as it develops in the womb is modeled in the form
`f(x) = 2^(kt)` , where T is the time in months. If the fetus is estimated to have 32 cells in the first month, how many cells does a newborn have on average?

Answer 1

• 2^45 or ≈ 3.5*10^13

Explanation:

Given equation

• f(t) = 2^(kt)
• f - number of cells, t - number of months, k- coefficient

We got 32 cells in the first month. It means:

• t = 1, f(1) = 32

Using these numbers we can find the coefficient k:

• 32 = 2^(k*1)
• 2^5 = 2^k
• k = 5

Then the equation becomes:

• f(t) = 2^(5t)

Average time is 9 months, we can calculate the number of cells:

• f(9) = 2^(5*9) = 2^45 ≈ 3.5*10^13