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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can you put the whole question here
Answer:
the partial derivatives are
fx =5/9
fy =(-13/18)
Step-by-step explanation:
defining the vector v (from (2,1) to (1,3))
v=(1,3)-(2,1) = (-1,2)
the unit vector will be
v'=(-1,2)/√5 = (-1/√5,2/√5)
the directional derivative is
fv(x,y) = fx*v'x + fy*v'y = fx*(-1/√5)+fy(2/√5) =-2/√5
then defining the vector u ( from (2, 1) toward the point (5, 5) )
u=(5,5)-(2,1) = (3,4)
the unit vector will be
u'=(3,4)/5 = (3/5,4/5)
the directional derivative is
fu(x,y) = fx*ux + fy*uy = fx*(3/5)+fy(4/5)=1
thus we have the set of linear equations
-fx/√5*+2*fy/√5 =(-2/√5) → -fx + 2*fy = -2
(3/5) fx+(4/5)*fy=1 → 3* fx+4*fy = 5
subtracting the first equation twice to the second
3*fx+4*fy -(- 2fx)*-4*fy = 5 -2*(-2)
5*fx=9
fx=5/9
thus from the first equation
-fx + 2*fy = -2
fy= fx/2 -1 = 5/18 -1 = -13/18
thus we have
fx =5/9
fy =(-13/18)
Answer:
Harry is 2, Jim is 6
Step-by-step explanation:
The first statement tells us they are 4 years part. Then you need to find two numbers that are 4 apart and that has one that is half the other, like 4 and 8. Finally, subtract two because this will happen in two years and you need their ages now.
Sorry if this was confusing.
y = -4x + 5
y = 1/4x + 5
y = 4x - 5
Answer:
y=-4x + 3
Step-by-step explanation:
its the only one with a negative slope
(e) - f(x)
(b) f(3)
(f) f(x+3)
(c) f(-3)
(g) f(3x)
(d) f(-x)
(h) f(x+h)
(a) f(0) = (Simplify your answer.)
(b) f(3) = (Simplify your answer.)
(c) f(-3)=(Simplify your answer.)
Answer:
f(0)=2
f(3)=14
f(3)=14