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Logarithms:

The number of cells in an embryo as it develops in the womb is modeled in the form [tex]f(x) = 2^{kt}[/tex] , 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?

Respuesta :

mhanifa

Answer:

  • 2^45 or ≈ 3.5*10^13

Step-by-step 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

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