Answer:
3.85 hours
Step-by-step explanation:
We have that the model equation in this case would be of the following type, being "and" the concentration of bacteria:
y = a * e ^ (b * t)
where a and b are constants and t is time.
We know that when the time is 0, we know that there are 100,000 bacteria, therefore:
100000 = a * e ^ (b * 0)
100000 = a * 1
a = 100000
they tell us that when the time is 2 hours, the amount doubles, that is:
200000 = a * e ^ (b * 2)
already knowing that a equals 100,000
e ^ (b * 2) = 2
b * 2 = ln 2
b = (ln 2) / 2
b = 0.3465
Having the value of the constants, we will calculate the value of the time when there are 380000, that is:
380000 = 100000 * (e ^ 0.3465 * t)
3.8 = e ^ 0.3465 * t
ln 3.8 = 0.3465 * t
t = 1.335 / 0.3465
t = 3.85
That is to say that in order to reach this concentration 3.85 hours must pass
Answer:
x = 3.1 %
Step-by-step explanation:
Let x be the slope the track.
Given:
Distance between station A and B = 270 ft
Track rise = 
We need to find the slope of the railway track between station A an B.
Solution:
The maximum grade allowed between two stations in a rapid-transit rail system is 3.5%.
We know that slope of the railway track is equal to gradient of the tracks.
So. the slope of the railway track is defined as the ratio of the distance between the stations and track rises.


x = 3.1 %
So x = 3.1 % less than the maximum grade allowed between two stations in a rapid-transit rail system is 3.5%.
Therefore, x = 3.1 % meets the rapid-transit rail standards.
For this case we have the following expression:

From here, we must clear the value of a.
We then have the following steps:
Place the terms that depend on a on the same side of the equation:

Do common factor "a":

Clear the value of "a" by dividing the factor within the parenthesis:

Answer:
The clear expression for "a" is given by:

8x-10=3x+90
5x=100
X=20
B=3(20)+90=150