Question

25. A post-doctoral research student is working with a culture of bacteria that doubles in size every 72 hours. The initial population count was 750 bacteria. Rounding to five significant digits, write an exponential equation representing this situation. To the nearest whole number, what is the population size after 30 days?

Answer 1

Answer:

$P=750 e^{0.00963t}$

The population size would be 753,190 after 30 days

Explanation:

Since, the population growth function is,

$P = P_0 e^{rt}$

According to the question,

if t = 0, P = 750,

$\implies 750 = P_0 e^0\implies P_0 = 750$

Also, if t = 72, P = 1500,

$\implies 1500 = P_0 e^{72r}\implies 1500 = 750 e^{72r}\implies 2 = e^{72r}\implies \ln 2 = 72r\implies r = \frac{\ln 2}{72}\approx 0.00963$

Hence, the required function would be,

$P=750 e^{0.00963t}$

If t = 720 hours  ( 30 days = 720 hours ),

Then, the population after 30 days would be,

$P=750 e^{0.00963\times 720}=750 e^{6.912}=753190.30695\approx 753190$