Question

The population of a culture of bacteria, P(t), where t is time in days, is growing at a rate that is proportional to the population itself and the growth rate is 0.2. The initial population is 10.(1) What is the population after 50 days? (Do not round your answer.)

Answer 1

Okay, here we have this:

Considering the provided information, we are going to calculate the requested population, so we obtain the following:

Then we will substitute in the following exponential growth formula:

$n(t)=n_0(1+r)^t$

Then, replacing:

$\begin{gathered} n(50)=10(1+0.2)^{50} \\ n(50)=10(1.2)^{50} \\ n(50)\approx91004.38 \end{gathered}$

Finally we obtain that the population will be approximately 91004.38 after 50 days.