Question

急!!!!!数学题(英文的)

A bacteria culture grows with constant relative growth rate. After 2 hours there are 600 bacteria and after 8 hours the count is 75,000.
(a) Find the initial population
P(0) =______bacteria

(b) Find an expression for the population after t hours.
P(t) = ______

(c) Find the number of cells after 3 hours.
P(3) =_____bacteria

(d) Find the rate of growth after 3 hours.
P'(3) = ________bacteria/hour

(e) When will the population reach 200,000?
t =_____ hours

谢谢大家了!!!
我是不知道答案怎么求....不是看不懂题.

dP(t)/dt = kP(t).
P(t)=Ae^(kt).
K和A是多少?

Answer 1

Solution:

The rate of population growth is proportional to the current population, i.e.,

dP(t)/dt = kP(t).

Solve the differential equation, we get the general solution

P(t)=Ae^(kt).

Then, based on the given condition, we have

600 = Ae^(2k),
75000 = Ae^(8k).

Solve the equations for A and k

A = 120,
k = 0.8047.

and we get the bacteria population as a function of time.

I suppose you are able to finish it from here.

Good luck!

Answer 2

奥数题吧，题不难！但根本看不懂！

Answer 3

细菌文化增长与恒定的相对增长率。 在2个小时以后有600细菌，并且在8个小时以后计数是75,000。
(a)寻找最初的人口
P (0) =______bacteria

(b)在t小时以后发现人口的一个表示。
P (t) = ____

(c)在3个小时以后看到细胞的数量。
P (3) =_____bacteria

(d)在3个小时以后发现增长率。
P'(3) = ________bacteria/hour

(e)人口何时将到达200,000 ？
t =___小时
翻译过来了可以了吗？？