Population growth
the number of a certain type of bacteria increases continuously at a rate proportional to the number present. there are 150 bacteria at a given time and 450 bacteria 5 hours later.
(a) how many bacteria will there be 10 hours after the initial time?
(b) how long will it take for the population to double?
(c) does the answer to part (b) depend on the starting time? explain your reasoning.

Step-by-step explanation:

Given that the number of a certain type of bacteria increases continuously at a rate proportional to the number present.

Initial population = 150

Hence equation for population P would be

where t = time in hours

When t=5, P = 450

Substitute to get

k=0.2197

is P(t)

P will double when

t =3.155

Between 3rd and 4th it would double

c) Yes it doubles when 3.155 hours lapsed from the start time since t in the equation is time lapsed from start time.

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

wth is with the little mtn top and what are you talking about like fix your words and accually make sence with them and i like was in a completly different question like three times like it seems like your ilitteret