WORK THIS PROBLEM : The biomass of a yeast culture in an experiment is initially

Question

WORK THIS PROBLEM:

The biomass of a yeast culture in an experiment is initially 29 grams. After 30 minutes the mass is 37 grams. Assuming that the equation for unlimited population growth gives a good model for the growth of the yeast when the mass is below 100 grams, how long will it take for the mass to double from its initial value?

(Use the given information to solve for the proportionality constant “k”. Then substitute this value for “k” in the model y = y0ekt. Now use the model to answer the question being asked.)

Explanation / Answer

y=y0ekt

t=30 mins=0.5 hours

37=29e0.5k

ln(37/29)=0.5k

k=0.487

58=29e0.487t

ln 2=0.487t

t=1.423 hours

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