Question

QUESTION 16. 1 POINTA sample of bacteria is growing at an hourly rate of 5% according to the continuous exponential growth function. Thesample began with 10 bacteria.How many bacteria will be in the sample after 28 hours? Round your answer down to the nearest whole number.Provide your answer below

Answer 1

We can express the exercise in terms of a function

$n(t)=n_0\cdot e^{rt}$

Where

n is the number of bacterias

t is the time

r is the relative rate of growth

From the problem we have

$n(t)=10\cdot e^{0.05t}$

if t=28

$\begin{gathered} n(28)=10\cdot e^{0.05(28)} \\ n(28)=10\cdot e^{1.4} \\ n(28)=40.552 \end{gathered}$

After 28 hours will be 40 bacterias