Question

The population P of a culture of bacteria is described by the equation P left parenthesis t right parenthesis equals 1200 e to the power of 0.052 t end exponent, where t is the time, in hours, relative to the time at which the population was 1200. What was the population at t = 6 hours?

Answer 1

as per question statement

we need to set up an equation first

`p(t)=1200e^(0.052*t)`

they have given that it is relative to 1200 that means it starts to increase from 1200 at t=0 initially 1200 bacteria were present

we need to find population at t=6

we need to plug t=6 in p(t).

`P(6)=1200e^(0.052*6)=1639.38`

1638.38 bacteria were present at that time t=6