A population of bacteria in a laboratory culture is being monitored. The number of bacteria, $B$ , in the culture, $t\,$ hours after the initial observation, is modelled by the equation

\frac{400e^{kt}}{7 + e^{kt}}

where $k\,$ is a constant.

Find the number of bacteria in the culture at the start of the study.

Given that there are 160 bacteria in the culture after 5 hours,

show that $k=15ln⁡(143)\displaystyle k = \frac{1}{5}\ln\left(\frac{14}{3}\right)$ .

Given also that, when $t = T$ , the number of bacteria is increasing at a rate of 25 per hour,

find the possible values of $T$ , giving your answers to one decimal place.

A population of bacteria in a laboratory culture is being monitored. The number of bacteria, $B$ , in the culture, $t\,$ hours after the initial observation, is modelled by the equation

\frac{400e^{kt}}{7 + e^{kt}}

where $k\,$ is a constant.

Find the number of bacteria in the culture at the start of the study.

Given that there are 160 bacteria in the culture after 5 hours,

show that $k=15ln⁡(143)\displaystyle k = \frac{1}{5}\ln\left(\frac{14}{3}\right)$ .

Given also that, when $t = T$ , the number of bacteria is increasing at a rate of 25 per hour,

find the possible values of $T$ , giving your answers to one decimal place.

Integration

Question 41

Markscheme

Integration

Question 41

Markscheme

Integration

Question 41

Integration Questions

Integration

Question 41

Integration Questions