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Zolol [24]
2 years ago
5

2. Bacterial Culture Problem: When you grow a

Mathematics
1 answer:
nignag [31]2 years ago
6 0

The area is changing at an increasing rate because the values of A(0), A(5), and A(10) increases as t increases

<h3>Find the area at times t = 0, t = 5, and t = 10.</h3>

The function is given as:

A(t) = 9 * (1.1)^t

Substitute t = 0, t = 5, and t = 10.

A(0) = 9 * (1.1)^0 = 9

A(5) = 9 * (1.1)^5 = 14.5

A(10) = 9 * (1.1)^10 = 23.3

The area is changing at an increasing rate because the values of A(0), A(5), and A(10) increases as t increases

<h3>Use the results of part a to find the radius of the culture at these three times</h3>

The area of a circle is

A = πr^2

Make r the subject

r = √(A/π)

So, we have:

r = √(9/π) =  1.7

r = √(14.5/π) =  2.1

r = √(23.3/π) =  2.7

The radius is changing at an increasing rate

<h3>Write an equation for the composite function R(A(t)).</h3>

In (b), we have:

r = √(A/π)

Express as a function

r(A(t)) = √(A/π)

Hence, the equation for the composite function is R(A(t)) = √(A/π)

<h3>The restriction for the function R * A</h3>

We have:

r(A(t)) = √(A/π)

A(t) = 9 * (1.1)^t

This gives

r(A(t)) = √(9 * (1.1)^t/π)

The radius is 30.

So, we have:

√(9 * (1.1)^t/π) = 30

Square both sides

(9 * (1.1)^t/π)= 900

Divide by 9

(1.1)^t/π= 100

Multiply by π

(1.1)^t= 314

Take the logarithms of both sides

t * log(1.1) = log(314)

Solve for t

t = 60

Hence, the restriction on the domain is 0 <= t <= 60

Read more about composite functions at:

brainly.com/question/13502804

#SPJ1

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const2013 [10]

Answer:

  an = -3·2^(n-1)

Step-by-step explanation:

The first term is a1 = -3.

The common ratio is r = -6/-3 = 2.

The given formula tells you the formula for this sequence is ...

  an = -3·2^(n-1)

3 0
2 years ago
Find g(4x)<br> g(x)=x²-4
7nadin3 [17]

Answer:

g(x) = x² - 4 is already in form of a variable, I.e., x

g(4x) takes another variable, I.e., 4x

Same as before, 4x takes over x:

=> g(4x) = (4x)² - 4

  • <em>(</em><em>ax</em><em>)</em><em>²</em><em> </em><em>=</em><em> </em><em>a</em><em>²</em><em>x</em><em>²</em><em>,</em><em> </em><em>where</em><em> </em><em>a</em><em> </em><em>is</em><em> </em><em>some</em><em> </em><em>arbitrary</em><em> </em><em>constant</em><em>.</em><em> </em>

<h3><u>Answer</u><u>:</u> </h3>

=> g(4x) = 16x² - 4

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3 0
2 years ago
Read 2 more answers
10 points! I will thanks, rate, and give best answer!!
vfiekz [6]
Answer: The fourth term is -102

----------------------------------------------

Explanation:

The term after the nth term is generated by this rule  a_{n+1} = -4(a_n) + 2 which means that we first
Step 1) multiply the nth term ( a_n ) by -4
Step 2) Add the result of step 1 to the value 2 to get the next term in the sequence

Let's follow those steps above to generate the first four terms

The first term is a_1 = 2. In short, the first term is 2

The second term is...
a_{n+1} = -4(a_n) + 2
a_{1+1} = -4(a_1) + 2
a_{2} = -4(2) + 2
a_{2} = -8 + 2
a_{2} = -6
So the second term is -6

The third term is...
a_{n+1} = -4(a_n) + 2
a_{2+1} = -4(a_2) + 2
a_{3} = -4(-6) + 2
a_{3} = 24 + 2
a_{3} = 26
The third term is 26

Finally, the fourth term is...
a_{n+1} = -4(a_n) + 2
a_{3+1} = -4(a_3) + 2
a_{4} = -4(26) + 2
a_{4} = -104 + 2
a_{4} = -102
The fourth term is -102.
4 0
3 years ago
1,2,4,7,11,16,22, ___,____<br> What is the rule?
Paha777 [63]
Find rates of change until you find a constant.

dy/dx=1,2,3,4,5,6

d2y/dx2=1,1,1,1,1  

So the acceleration, d2y/d2x, is constant.  This means that this is a quadratic sequence of the form a(n)=an^2+bn+c.  So we can set up a system of equations to solve for the values of a,b, and c.  Using the first three points, (1,1), (2,2), and (3,4) we have:

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2a=1, so a=1/2 making 5a+b=2 become:

2.5+b=2, so b=-1/2, making a+b+c=1 become:

1/2-1/2+c=1, so c=1  so the rule is:

a(n)=0.5x^2-0.5x+1  or if you prefer to not have decimals

a(n)=(x^2-x+2)/2
6 0
3 years ago
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AnnyKZ [126]
Is there a picture to show it?
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