Question #a1b58

1 Answer

Since the yeast divides every two hours, its population (and hence yeast mass) doubles every two hours. Because the doubling time is a constant it is exponential growth.

The mass of yeast grows exponentially with time as :
m(t)=moexp(λt);    λ=ln(2)τ,
where λ is the growth factor and τ is the doubling time.
We are given the doubling time (τ) and the initial mass m0 and are asked to estimate t for m(t) to reach the value of the mass of a typical human. Let us assume 75 kg as the mass of a typical human, so m(t)=75 kg.

τ=2hrs    λ=0.3465hr1;    t=?
m0=60pg=6.0×1014kg,    m(t)=75kg

m(t)=moexp(λt);    t=ln(m(t)mo)λ=ln(m(t)mo)ln(2)τ

If your calculator struggles to evaluate the logarithm of such a large number you may have to assist it. Remember the following results,

ln(ab)=ln(a)+ln(b) and ln(xy)=yln(x).

Use these to write ln(12.5×1014) as ln(12.5)+14ln(10)
ln(m(t)mo)=34.7619;    t=34.7619ln(2)×2hrs=100.3 hrs.

So it takes 100.3 hrs, which is approximately, 4 days and 4 hours for the yeast to grow to the mass of a typical human.