Answer: 380000 cells/hour
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).
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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b. rhombus
c. square
d. trapezoid
Answer:
parallelogram
Step-by-step explanation:
b. Use the property b*b b to express xy in terms of b, p, and q
c. Compute log b(xy) and simplify
Answer with Step-by-step explanation:
a.
Taking both sides log
Using identity:
Using identity:
b.
We know that
Using identity
c.
Substitute the values then we get
By using
Hence,
To prove the property log b(xy) = log bx + log by, we let x = and y = , express xy in terms of the base b and the exponents p and q, and then use the properties of logarithms to show the equality.
The student is asking to prove the logarithmic property − log b(xy) = log bx + log by. Here's a step-by-step explanation:
Let x = bp and y = bq. To solve for p and q, take the logarithm base b of both sides. Thus, p = logbx and q = logby.
Using the property of exponents, xy = bp*bq = bp+q.
Now compute logb(xy). According to the logarithmic property, logb(bp+q) = p + q. Since p = logbx and q = logby, then logb(xy) = logbx + logby.
Therefore, we have proven the given logarithmic property using the steps provided in the question.
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Answer:
f(n)= (n-50)²
Step-by-step explanation:
The difference between a number n and fifty:
Square of this difference:
It would look like this as variable expression:
What percent of the carbon-14 had been lost from the pollen?
(half-life of carbon-14 = 5730)