Please help me! thank you so much

If 3,000 bacteria, with a growth constant (k) of 2.8 per hour, are present at the beginning of an experiment, in how many hours

Ivenika [448]

Given:

Initial number of bacteria = 3000

With a growth constant (k) of 2.8 per hour.

To find:

The number of hours it will take to be 15,000 bacteria.

Solution:

Let P(t) be the number of bacteria after t number of hours.

The exponential growth model (continuously) is:

$P(t)=P_0e^{kt}$

Where, $P_0$ is the initial value, k is the growth constant and t is the number of years.

Putting $P(t)=15000,P_0=3000, k=2.8$ in the above formula, we get

$15000=3000e^{2.8t}$

$\dfrac{15000}{3000}=e^{2.8t}$

$5=e^{2.8t}$

Taking ln on both sides, we get

$\ln 5=\ln e^{2.8t}$

$1.609438=2.8t$ $[\because \ln e^x=x]$

$\dfrac{1.609438}{2.8}=t$

$0.574799=t$

$t\approx 0.575$

Therefore, the number of bacteria will be 15,000 after 0.575 hours.

4 0

2 years ago

In a 45 45 90 right angle what is the ratio of the length of one leg to the length of the other

Eva8 [605]

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5 0

3 years ago

A walkway forms one diagonal of a square playground. The walkway is 18 m long.

olga55 [171]

18m x 4 = 72m

Walkway = 72 meters.

6 0

3 years ago

One member of the debate team is going to be chosen president. each member is equally likely to be chosen. the probability that

inessss [21]

Let
x-------> the probability that a boy is chosen
B------> number of boys in the debate team
G------> number of girls in the debate team

we know that
B+G=20-----> G=20-B-----> equation 1
probability that a boy is chosen=number of boys in the debate team/total of people
so
x=B/20-------> equation 2

the probability that a girl is chosen is 2/3 the probability that a boy is chosen
probability that a girl is chosen=(2/3)*x
probability that a girl is chosen=G/20
(2/3)*x=G/20-----> equation 3
substitute equation 1 in equation 3
(2/3)*x=[20-B]/20----> equation 4

resolve the equations system
x=B/20
(2/3)*x=[20-B]/20

using a graph tool
see the attached figure
the solution is
x=0.6
B=12
G=20-12-----> G=8

number of boys in the debate team is 12
number of girls in the debate team is 8
the probability that a boy is chosen is 0.6 ----> 60%
the probability that a girl is chosen is 0.6*(2/3)----> 0.4---> 40%

the answer is
number of girls in the debate team is 8