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kipiarov [429]
3 years ago
10

The expression 3 ( 1 . 5 )^ t models the number of bacteria in a culture as a function of the number of hours since the culture

was created.
What does 3 represent in this expression?

A- There were initially 3 bacteria in the culture.

B- The culture was created 3 hours ago.

C-The number of bacteria is multiplied by 3 each hour.
Mathematics
1 answer:
Masteriza [31]3 years ago
4 0

Answer:

A

Step-by-step explanation:

Given

3(1.5)^{t}

When the culture was created t = 0, thus

3(1.5)^{0} = 3 × 1 = 3

That is there were initially 3 bacteria in the culture → A

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For the composite function, identify an inside function and an outside function and write the derivative with respect to x of th
alexira [117]

Answer:

The inner function is h(x)=4x^2 + 8 and the outer function is g(x)=3x^5.

The derivative of the function is \frac{d}{dx}\left(3\left(4x^2+8\right)^5\right)=120x\left(4x^2+8\right)^4.

Step-by-step explanation:

A composite function can be written as g(h(x)), where h and g are basic functions.

For the function f(x)=3(4x^2+8)^5.

The inner function is the part we evaluate first. Frequently, we can identify the correct expression because it will appear within a grouping symbol one or more times in our composed function.

Here, we have 4x^2+8 inside parentheses. So h(x)=4x^2 + 8 is the inner function and the outer function is g(x)=3x^5.

The chain rule says:

\frac{d}{dx}[f(g(x))]=f'(g(x))g'(x)

It tells us how to differentiate composite functions.

The function f(x)=3(4x^2+8)^5 is the composition, g(h(x)), of

     outside function: g(x)=3x^5

     inside function: h(x)=4x^2 + 8

The derivative of this is computed as

\frac{d}{dx}\left(3\left(4x^2+8\right)^5\right)=3\frac{d}{dx}\left(\left(4x^2+8\right)^5\right)\\\\\mathrm{Apply\:the\:chain\:rule}:\quad \frac{df\left(u\right)}{dx}=\frac{df}{du}\cdot \frac{du}{dx}\\f=u^5,\:\:u=\left(4x^2+8\right)\\\\3\frac{d}{du}\left(u^5\right)\frac{d}{dx}\left(4x^2+8\right)\\\\3\cdot \:5\left(4x^2+8\right)^4\cdot \:8x\\\\120x\left(4x^2+8\right)^4

The derivative of the function is \frac{d}{dx}\left(3\left(4x^2+8\right)^5\right)=120x\left(4x^2+8\right)^4.

3 0
3 years ago
Find the product.<br> (x+2)(x−2)=
kaheart [24]

Answer:

x² - 4

Step-by-step explanation:

Step 1: Write expression

(x + 2)(x - 2)

Step 2: FOIL

x² + 2x - 2x - 4

Step 3: Combine like terms

x² - 4

8 0
3 years ago
Read 2 more answers
Which of the following is true of the constructions of an equilateral triangle, a square, and a regular hexagon when they are in
lidiya [134]
<span>a regular hexagon inscribed in a circle </span>
6 0
3 years ago
One garden had 5 times as many raspberry bushes as a second garden. After 22 bushes are transplanted from the first garden to th
Aleonysh [2.5K]

Let the number of raspberry bushes in one garden = x

And the number of raspberry bushes in second garden = y

Garden one has 5 times as many raspberry bushes as second garden,

So the equation will be,

x = 5y -------(1)

If 22 bushes were transplanted from garden one to the second, number of bushes in both the garden becomes same,

Therefore, (x - 22) = (y + 22)

x - y = 22 + 22

x - y = 44 ------(2)

Substitute the value of x from equation (1) to equation (2)

5y - y = 44

4y = 44

y = 11

Substitute the value of 'y' in equation (1),

x = 5(11)

x = 55

Therefore, Number of bushes in garden one were 55 and in second garden 11 originally.

Learn more,

brainly.com/question/12422372

5 0
3 years ago
Jordan is a teacher and takes home 40 papers to grade over the weekend. He can grade at a rate of 6 papers per hour. How many pa
Mazyrski [523]

Answer:

10

Step-by-step explanation:

6x5=30

40-30=10

6 0
3 years ago
Read 2 more answers
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