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PLEASE HELP AND THANK YOU​

PLEASE HELP AND THANK YOU​-example-1
User Yewande
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Answer:

• n(t) = 150·2^t . . . . . . . . . . . . number of cells after t minutes

• a(t) = π(0.25 +0.50t)^2 . . . . area in cm^2 after t minutes

• d(t) = n(t)/a(t) = (2400·2^t)/(π(1+2t)^2)

Explanation:

The number of cells (n(t)) is described by an exponential function of time (t) with an initial value of 150 and a growth factor of 2 each minute:

n(t) = 150·2^t . . . . . . n in cells; t in minutes

___

The area of the culture is given by ...

a(t) = π·(r(t))^2 . . . . where r(t) is the radius as a function of time.

The radius is linearly increasing with a rate of increase of 0.50 cm/min, so can be described by ...

r(t) = 0.25 +0.50t

Then the area is ...

a(t) = π·(0.25 +0.50t)^2

A factor of 0.25 can be removed from inside parentheses to make this be ...

a(t) = (π/16)(1 +2t)^2 . . . . . a in cm^2; t in minutes

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The density is the number of cells divided by the area:

d(t) = n(t) / a(t) = 150·2^t/((π/16)(1 +2t)^2)

Simplifying a bit, this is ...

d(t) = (2400/π)(2^t)/(1 +2t)^2 . . . . . d in cells/cm^2; t in minutes

User ScootyPuff
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