A certain bacteria population is known to quadruples every 150 minutes. Suppose that there are initially 200 bacteria. What is the size of the population after t hours?

Answers

Answer 1

Answer: This is a geometric progression
The size of the population afeter t hours will be=a₁*r^n

a₁= the first term =200
r=common ratio=4

150 minutes=150 minutes * (1 hour /60 minutes)=2.5 hours.

In this case:
the size of the populatation after t hours=200*4^t/2.5=200*4^0.4t

To check
t=0⇒ the size will be=200*4⁰=200*1=200
t=2.5 hours=150 minutes; the size will be =200*4¹=800
t=5 hours; the size will be=200*4²=200*16=3200

Answer: the size will be= 200*4^(0.4t)

Answer 2

Answer:

Final answer:

The growth of the bacteria is represented by the exponential growth equation. Given the initial population, the four-fold increase, and the time interval for the increase, we can find the population after any given time by using the equation P = 200 * 4^(t/2.5).

Explanation:

The problem given is an example of an exponential growth problem. For these types of problems, we use the formula P = P0 * e^(kt), where P is the final population, P0 is the initial population, k is the growth rate, and t is time. However, in this case, we were given that the bacteria quadruples, meaning 'quadrupling' is not a continuous rate, so we use a slightly different form of the equation: P = P0 * (b)^(t/t0), where b is the times increase and t0 is the time interval for the b-fold increase.

Given that the initial population P0 is 200 bacteria, b is 4 because the population quadruples every 150 minutes, and time t0 is 150 minutes or 2.5 hours. We need to find the population P after t hours. Substituting these values into our equation gives us: P = 200 * 4^(t/2.5).

So, after t hours, the population of the bacteria will be given by the equation P = 200 * 4^(t/2.5).

Learn more about Exponential Growth here:

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Solutions for 12 – x2 = 0?

Multiply. Write your answer in simplest form.

5/12 x 4/5

Answers

Multiply across.
Step 1: 5x4=20
Step 2: 12x5=60
Step 3: Reduce or simplify
20/60=1/3

You reduce the fraction by dividing numerator and denominator by 5.
1/12 x 4.Reduce the fraction by dividing numerator and denominator by 4.
1/3 x 1.You multiply the values. 1/3.

In 36 days a girl spent 18 dollars. On average, what did she spend daily?

Answers

On average, she spent 18/36 = 0.5$

Find the value of x in this polygon.

Answers

Answer:

Step-by-step explanation:

you have to add to 180 and 68+112=180

Final answer:

To find the value of x in the polygon, you need more information such as one of the interior angles or the total sum of the interior angles.

Explanation:

To find the value of x in this polygon, you need to use the fact that the sum of all interior angles in a polygon is given by the formula (n-2) * 180 degrees, where n is the number of sides. In this case, since it is not mentioned what polygon it is, we will assume it is a regular polygon. If the polygon is regular and has x sides, then the sum of all interior angles is also (x-2) * 180 degrees. To find the value of x, you would need more information, such as one of the interior angles or the total sum of the interior angles.