Aculture of yeast grows at a rate proportional to its size. if the initial population is 3000 cells and it doubles after 2 hours, answer the following questions.
(a) write an expression for the number of yeast cells after t hours.
(b) find the number of yeast cells after 8 hours.
(c) find the rate at which the population of yeast cells is increasing at 8 hours.

The expression for the number of yeast cells after t hours is 3000 + 2t

The number of yeasts cells after 88 hours is 3016 yeasts.

The rate at which the population of yeast cells is increasing at 8 hours is 377 yeasts per hour.

The expression for the number of yeast cells after t hours will be:

= 3000 + (2 × t)

= 3000 + 2t

The number of yeast cells after 8 hours will be:

= 3000 + 2t

= 3000 + 2(8)

= 3000 + 16

= 3016

The rate at which the population of yeast cells is increasing at 8 hours will be: = 3016/8 = 377

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a) C(t) = 3000e^(rt)

b) C(8) = 47400 yeast cells.

c) 13870 yeast cells a hour.

Step-by-step explanation:

The growth of the culture of yeast in hours can be modeled by the following differential equation:

1) dC/dt = rC,

where C is the number of cells and r is the growth rate.

For question a), to write an expression for the number of yeast cells after t hours, we need to solve the differential equation 1). I am going to solve it by the variable separation method.

dC/C = rdt

Integrating both sides, we have:

ln C = rt + C0

where C0 is the initial population of cells.

We need to isolate C in this equation, so we do this

e^(ln C) = e^(rt + C0)

So

C(t) = C0e^(rt)

The initial population of cells is given as 3000, so:

C(t) = 3000e^(rt)

b)

After two hours, the number of cells grows. So C(2) = 6000. This is helpful so we can find the growth rate r.

6000 = 3000e^(2r)

e^(2r) = 2

ln(e^(2r)) = ln 2

2r = 0.69

r = 0.345

Now we have C(t) = 3000e^(0.345t), so

C(8) = 3000e^(0.345*8) = 47400 yeast cells.

c)

C(7) = 3000e^(0.345*7) = 33570 yeast cells.

C(8) - C(7) = 47400 - 33570 = 13870 yeast cells. So, at 8 hours, the population of yeast cells is increasing at the rate of 13870 yeast cells a hour.

2cm

Step-by-step explanation:

First, it is important to define both the radius and diameter. A diameter is the length of a line through the center of a circle that touches two points on the edge.

In the semicircle on the top, if we can imagine it making up a full circle, we can note that the bottom center of the semicircle is the center of the full circle, with the line of length 4cm going right through it. Similarly, for the bottom semicircle, as the line between the semicircles is straight, the diameter for that one is 4cm as well.

The radius is equal to half of the diameter. The diameter is 4cm, so the radius is 4cm/2 = 2cm