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Jobisdone [24]
3 years ago
13

The corporate team-building event will cost $8 if it has 4 attendees. How many attendees can

Mathematics
1 answer:
sukhopar [10]3 years ago
8 0
Answer: 22 attendees can attend the corporate team-building event, with a budget of $46.

1. 8 = 4x
2. 8/4 = 4x/4
3. x = 2, each ticket would cost $2 per attendee
4. $46/$2 = 23
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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 complete question is added as an attachment

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

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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

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