1.6.8 Exponentials and logarithms

The population of a bacterial colony, $P$ , is being monitored in a laboratory. The number of bacteria is modelled by the equation

log_{10} P = 2 + 0.04t

where $t\,$ is the time in hours after monitoring began.

Use the equation of the model to answer parts (a) and (b).

Find the initial population of the bacterial colony.

[2]

After $T\,$ hours, the population reaches 500. Find the value of $T$ , giving your answer to 2 decimal places.

[3]

1.6.8 Exponentials and logarithms Questions

The population of a bacterial colony, $P$ , is being monitored in a laboratory. The number of bacteria is modelled by the equation

log_{10} P = 2 + 0.04t

where $t\,$ is the time in hours after monitoring began.

Use the equation of the model to answer parts (a) and (b).

Find the initial population of the bacterial colony.

[2]

After $T\,$ hours, the population reaches 500. Find the value of $T$ , giving your answer to 2 decimal places.

[3]