Using formula Nt = N0 x 2^n Calculate amount of time it takes for 1 cell that divide every 5 hours to make 8.8 x 10^14 cells

Question

When I try to calculate the log2 8.8 x 10^14 = n, I get approximately 50 divisions as my answer. Shouldn't I be able to get 8.8 x 10^14 if I now substitute 50 as n in 2^n power? I get a slightly larger number instead.

Answer 1

The DOUBLING period is 5 hours.  Then for t in HOURS,

 

N(t) = N₀ (2)^t/5

 

N₀ = initial population = 1

8.8 x 10¹⁴ = final population

 

Set the final population equal to N(t) and solve for t.

 

8.8 x 10¹⁴ = 1 (2)^t/5

 

log(8.8 x 10¹⁴) = (t/5) log2

 

t = 5 log(8.8 x 10¹⁴)/log2 hours ≅ 248.222 hours

 

Test the answer.

 

1 (2)^248.222/5 ≅ 8.799 x 10¹⁴,

 

which allowing for rounding, is 8.8 x 10¹⁴.

 

Answer 2

8.8 x 10¹⁴ = 2ⁿ

ln (8.8 x 10¹⁴) = n ln 2

 

Can you solve for n and answer?