Maths

The population, P, of bacteria in an experiment can be modelled by the formula P = 100e 0.4t ,
where t is the time in hours after the experiment began.
(a) Use the model to estimate the population of bacteria 7 hours after the experiment began.

(b) Interpret the meaning of the constant 100 in the model.

(c) How many whole hours after the experiment began does the population of bacteria first
exceed 1*million, according to the model?

What have you tried? Where are you stuck?

I'm, stuck on the first part at the moment.
I tried looking for a worked example and I found

P=100e^0.4t
P(7)=100e^2.8
=1644

No explanation, no nothing. So i'm confused how this answer was gotten, could you explain?.

At seven hours after the experiment began, t, by definition, is equal to 7. So all you need to do is substitute t = 7 in the given formula P = 100e^(0.4t).

Well thats just
P = 100e^2.8 then right? is there nothing I must do further?

No, apart from determining and stating the numerical value.

Which would be?

You quoted it yourself in post #3

But thats exactly what I don't understand, where did the 1644 come from? whats the working out behind it

You're supposed to use your calculator to find the numerical value of 100e^2.8