# Suppose that dP/dt = 0.19P(t) represents a mathematical model for the growth of a certain cell culture, where P(t) is the size of the culture (measured in millions of cells) at time t > 0 (measured in hours). How fast is the culture growing at the time t when the size of the culture reaches 2 million cells?

Step-by-step explanation:

Given that dP/dt = 0.19P(t)

where

P(t) is the size of the culture (measured in millions of cells) at time t > 0 (measured in hours).

The formula above represents a mathematical model for the growth of a certain cell culture. In essence, it represents the time rate of the growth of the cell culture, that is how fast the cell culture is growing.

Therefore, when P = 2 million cells:

dP/dt = 0.19 * 2000000 = 380000 cells/hour

Hence, the cell culture is growing at 380000 cells per hour.

The cell culture is growing at a rate of 0.38 million cells per hour when the size of the culture reaches 2 million cells. This is based on the given differential equation dP/dt = 0.19P(t).

### Explanation:

This problem is associated with the concept of differential equations, particularly exponential growth. In this scenario, the rate of change of P(t), the size of the cell culture, is given by the equation dP/dt = 0.19P(t). This can be interpreted as the culture is growing at 19% per unit of time.

To determine how fast the culture is growing when P(t) equals 2 million cells, we need to substitute 2 for P(t) in the given equation: dP/dt = 0.19*2. This calculation returns a value of 0.38 million cells per hour. Therefore, when the size of the culture reaches 2 million cells, it is growing at a rate of 0.38 million cells per hour.

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## Related Questions

The sum of three consecutive odd numbers is 69. What is the smallest of the three numbers?

21

Step-by-step explanation:

Let the smallest of the numbers be N

The other two numbers (consecutive) would be written as (n + 2), (n + 4)

Expressing these as an equation gives : (n) + (n+2) + (n+4) = 69

opening the bracket and collecting like terms, we have:

n+n+n+2+4=69

3n + 6 = 69

3n = 69 - 6

3n = 63

Dividing both sides by 3 or making n the subject formular, we get:

n = 63/3

n = 21.

Note, the other numbers are: 21, 23, and 25

They are all odd numbers

Their sum equals to 69

Eight times the difference of y and nine

Eight times the difference of y and nine will be 8(y - 9).

It should be noted that eight times the difference of y and nine simply means that one has to subtract 9 from y and then multiply the difference by 8.

Therefore, eight times the difference of y and nine will be 8(y - 9).

In conclusion, the correct option is 8(y - 9).

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(y-9)8

Step-by-step explanation:

you first solve 8-9, and then multiply is by 8.

Jack has a summer job caddying at a golf course. Jack earns $120a week. By rounding his weekly income to the nearest hundred dollars, find a reasonable estimate for his total income during the 12 week summer. A)$700
B) $800 C)$1200
D) $1700 ### Answers 1200 as you would round it down to 100 a week so you would do 100x12 6 apple trees fir every 4 pears trees How many apple trees would there be if there were 42 pear trees ### Answers Answer: 63 apple trees Explanation: divide 42 by 4 to get that amount of groups (10.5) then multiply that number by 6 so (10.5 • 6) and that should give the apple tree total. Please Help!!In 2010, Martin paid$5,518.00 in Social Security tax. The SS tax rate was 6.2%. What was Martin's taxable income in 2010?

$890 or it's$34211.6

Step-by-step explanation:

you divide 5518 by 6.2% or you multiply them

Solve this differential Equation by using power series
y''-x^2y=o

We're looking for a solution

which has second derivative

Substituting these into the ODE gives

Right away we see , and the coefficients are given according to the recurrence

There's a dependency between terms in the sequence that are 4 indices apart, so we consider 4 different cases.

• If , where is an integer, then

and so on, with the general pattern

• If , then

and so on, with

• If or , then

Then the solution to this ODE is