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3 years ago

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How do you solve this?

1 answer:

GrogVix [38]3 years ago

8 0

4x^3 square root 3b

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Suppose that a Petri dish initially contains 2000 bacteria cells. An antibiotic is introduced and after 4 hour, there are now 16

Sergeu [11.5K]

Answer:

a)The linear function for $P(t)$ is:

$P(t) = 2000 - 100*t$

b)The exponential function for $P(t)$ is:

$P(t) = 2000e^{-0.055t}$

Step-by-step explanation:

(a) Suppose that P(t) is a linear function. Find a formula for P(t):

$P(t)$ can be modeled by a linear function in the following format.

$P(t) = P_{0} - r*t$ , in which $P_{0}$ is the initial number of bacteria cells in the dish, t is the time and r is the rate that the number decreases.

Since the dish initially contains 2000 bacteria cells, $P_{0} = 2000$

We have

$P(t) = 2000 - r*t$

An antibiotic is introduced and after 4 hour, there are now 1600 bacteria cells present. So $P(4) = 1600$ . With this information, we can find the value of r.

$P(t) = 2000 - r*t$

$1600 = 2000 - r*(4)$

$4r = 400$

$r = \frac{400}{4}$

$r = 100$

So, the linear function for $P(t)$ is:

$P(t) = 2000 - 100*t$

b) Suppose that P(t) is an exponential function. Find a formula for P(t)

$P(t)$ can also be modeled by an exponential function in the following format:

$P(t) = P_{0}e^{rt}$

The values mean the same as in a). We use the fact that $P(4) = 1600$ to find r.

$P(t) = 2000e^{rt}$

$1600 = 2000e^{4r}$

$e^{4r} = \frac{1600}{2000}$

$e^{4r} = 0.8$

$ln e^{4r} = ln 0.8$

$4r = -0.22$

$r = \frac{-0.22}{4}$

$r = -0.055$

So, the exponential function for $P(t)$ is:

$P(t) = 2000e^{-0.055t}$

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4 years ago

Which expression represents the phrase "twice the difference of a number and 5"?

Molodets [167]

Answer:

2 (x - 5)

I hope this helps u.

Step-by-step explanation:

8 0

3 years ago

Compare and contrast a triangular prism and a triangular pyramid. In your response, include the shape and number of bases, and t

Firlakuza [10]

A great way to organize this would be to make a t-chart!

<u>Triangular Prism | Triangular Pyramid
</u> |
<u />*2 triangular bases | *1 triangular base
|
*3 lateral faces in the | * 3 lateral faces in the
shape of rectangles | shape of triangles

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3 years ago

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A storage container is shaped like a rectangular prism. The volume of the container is 2415 cubic feet. The area of the base of

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Answer:

11.5 feet

Step-by-step explanation:

To solve this question first you take the volume which is 2415 and divide it by 210 to get your answer as 11.5 feet

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4 years ago

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How do I determine the slope of the line using a graph

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It's hard to explain, but theres a trick to it too.

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