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george has opened a new store and he is monitoring its success closely. He has found that this store’s revenue each month can be modeled by r(x)=x2+5x+14 where x represents the number of months since the store opens the doors and r(x) is measured in hundreds of dollars. He has also found that his expenses each month can be modeled by c(x)=x^2−4x+5 where x represents the number of months the store has been open and c(x) is measured in hundreds of dollars.

the new store will sell 900 items in its fifth month in business

the store will have a profit of $900 after its fifth month in business

the store will have a profit of $5400 after its fifth month in business

the new store will sell 5400 items in its fifth month in business

Step-by-step explanation:

The correct answer is that the new store will have a profit of $5400 after its fifth month.

Profit is given by subtracting revenue minus cost:

(R-C)(x) = (x²+5x+14)-(x²-4x+5) = x²-x²+5x--4x+14-5 = 5x+4x+14-5=9x+9

Using 5 for x,

(R-C)(5) = 9(5) + 9 = 45+9 = 54

This is in hundreds of dollars, so it represents $5400.

is there any attachment? what are the equations?

answer: solve 5\cdot 2^x=2405⋅2  

x

=2405, dot, 2, start superscript, x, end superscript, equals, 240.

solution

to solve for xxx, we must first isolate the exponential part. to do this, divide both sides by 555 as shown below. we do not multiply the 555 and the 222 as this goes against the order of operations!

\begin{aligned} 5\cdot 2^x& =240 2^x& =48 \\ \end{aligned}  

5⋅2  

x

2  

x

​    

=240

=48

​

step-by-step explanation: