QUESTION 1 The profit P (in hundreds of dollars) that a company makes depends on

Question

QUESTION 1
The profit P (in hundreds of dollars) that a company makes depends on the amount x (in hundreds of dollars) the company spends on advertising according to the model. P(x) = 230 + 40x - 0.5x2 What expenditure for advertising will yield a maximum profit?
40
0.5
230
20
QUESTION 2
The concentration C (in mg/dl), of a certain antibiotic in a patient's bloodstream is given by 50t/t^2+25 where t is the time (in hours) after taking the antibiotic. What is the concentration 10 hours after taking the antibiotic?
QUESTION 3
Write the logarithmic equation in exponential form.
Log2 16 = 4
QUESTION 4
Find the domain of the function: F(x) - 3/X
All real numbers
All real numbers except x=3
All positive real numbers
All real numbers except x=0
QUESTION 5
pH is a measure of the hydrogen ion concentration of a solution. It is defined as the negative logarithm of the hydrogen ion concentration. The equation is:

pH = - log [H+]

If an acid has an H+ concentration of 10-7, find the pH?
QUESTION 6
In order to join a movie streaming service, you pay a $75 annual fee, then $1.50 for each movie you stream. Which equation will allow you to determine the cost you will pay if you stream x number of movies? Select from the following equations and indicate the correct answer in the space below: 1st, 2nd, 3rd, or 4th.
QUESTION 7
Evaluate the function at the indicated value of x.

Function: f(x) = 0.5x Value: x = 2
QUESTION 8
Find the domain of the function f(x) = 7/6 - x

Domain: all real numbers x except x=7
Domain: all real numbers x except x=6
Domain: all real numbers x
Domain: all real numbers x except x = -6

QUESTION 9
Express the following matrix as a system of equations:
2 3 5
-4 7 2

QUESTION 10
Solve for x.

4x = 16

Explanation / Answer

Question1

a = 0.5 and b = 20, thus profit is maximized when

x = b /2a

= 20 /2(0.5) = 20.

Thus, profit is maximized when $2,000 is spent on advertising.

Question2

C(mg/dl)= 50 t / t^2 + 25

C(4)= 50(4) / 4^2 + 25 => 200/41 => 4.878 mg/dl

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