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3 years ago

What algebraic rule did you use to preform this translation????

Mathematics

1 answer:

Law Incorporation [45]3 years ago

5 0

Answer:

In geometry, a transformation is an operation that moves, flips, or changes a shape (called the preimage) to create a

new shape (called the image). A translation is a type of transformation that moves each point in a figure the same

distance in the same direction. Translations are often referred to as slides. You can describe a translation using words

like "moved up 3 and over 5 to the left" or with notation. There are two types of notation to know.

1. One notation looks like T(3, 5). This notation tells you to add 3 to the x values and add 5 to the y values.

2. The second notation is a mapping rule of the form (x, y) → (x−7, y+5). This notation tells you that the x and

y coordinates are translated to x−7 and y+5.

Step-by-step explanation:

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A bacteria culture starts with 400 bacteria and grows at a rate proportional to its size. After 4 hours, there are 9000 bacteria

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A) The expression for the number of bacteria is $P(t) = 400e^{0.7783t}$ .

B) After 5 hours there will be 19593 bacteria.

C) After 5.55 hours the population of bacteria will reach 30000.

Step-by-step explanation:

A) Here we have a problem with differential equations. Recall that we can interpret the rate of change of a magnitude as its derivative. So, as the rate change proportionally to the size of the population, we have

$P' = kP$

where $P$ stands for the population of bacteria.

Writing $P'$ as $\frac{dP}{dt}$ , we get

$\frac{dP}{dt} = kP$ .

Notice that this is a separable equation, so

$\frac{dP}{P} = kdt$ .

Then, integrating in both sides of the equality:

$\int\frac{dP}{P} = \int kdt$ .

We have,

$\ln P = kt+C$ .

Now, taking exponential

$P(t) = Ce^{kt}$ .

The next step is to find the value for the constant $C$ . We do this using the initial condition $P(0)=400$ . Recall that this is the initial population of bacteria. So,