Answer:
The change in revenue from the sale of one more doghouse if 110 doghouses have already been sold is dR/dx=66.67 $/doghouse.
Step-by-step explanation:
We have a revenue function that is:
We have to approximate the change in revenue from the sale of one more doghouse, if 110 doghouses have already been sold.
That is the marginal revenue at x=110.
The marginal revenue is expressed as the first derivative of the revenue.
Then, we calculate the derivative of R:
![\dfrac{dR}{dx}=\dfrac{d}{dx}[14,000\cdot \text{ln}(0.01x+1)]\\\\\\\dfrac{dR}{dx}=14,000\dfrac{d}{dx}[\text{ln}(0.01x+1)]\\\\\\\dfrac{dR}{dx}=14,000\cdot\dfrac{1}{0.01x+1}\cdot \dfrac{d}{dx}(0.01x+1)\\\\\\\dfrac{dR}{dx}=14,000\cdot\dfrac{1}{0.01x+1}\cdot 0.01\\\\\\\dfrac{dR}{dx}=\dfrac{14,000}{x+100}](https://tex.z-dn.net/?f=%5Cdfrac%7BdR%7D%7Bdx%7D%3D%5Cdfrac%7Bd%7D%7Bdx%7D%5B14%2C000%5Ccdot%20%5Ctext%7Bln%7D%280.01x%2B1%29%5D%5C%5C%5C%5C%5C%5C%5Cdfrac%7BdR%7D%7Bdx%7D%3D14%2C000%5Cdfrac%7Bd%7D%7Bdx%7D%5B%5Ctext%7Bln%7D%280.01x%2B1%29%5D%5C%5C%5C%5C%5C%5C%5Cdfrac%7BdR%7D%7Bdx%7D%3D14%2C000%5Ccdot%5Cdfrac%7B1%7D%7B0.01x%2B1%7D%5Ccdot%20%5Cdfrac%7Bd%7D%7Bdx%7D%280.01x%2B1%29%5C%5C%5C%5C%5C%5C%5Cdfrac%7BdR%7D%7Bdx%7D%3D14%2C000%5Ccdot%5Cdfrac%7B1%7D%7B0.01x%2B1%7D%5Ccdot%200.01%5C%5C%5C%5C%5C%5C%5Cdfrac%7BdR%7D%7Bdx%7D%3D%5Cdfrac%7B14%2C000%7D%7Bx%2B100%7D)
We then evaluate this marginal revenue at point x=110:
Answer:200,000
Step-by-step explanation:
If it increases 5% every year in 20 years it will Have increased 100% therefore the number would have doubled
Using the slope concept, it is found that the change in elevation was of -699 feet.
<h3>What is a slope?</h3>
The slope is given by the <u>vertical change divided by the horizontal change</u>, and it's also the tangent of the angle of depression.
In this problem, we have that:
- The vertical change is of h.
- The horizontal change is of 10,000 feet.
Hence:
tan(-4º) = h/10000
h = 10000 x tan(-4º)
h = -699.
More can be learned about the slope concept at brainly.com/question/18090623
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Answer:
C
Step-by-step explanation:
The line of best fit is a linear function that is closest to all the points and shows the trend in the data. Since the data is going up ultimately, the slope of the line will be positive. Only B and C are options.
To find the best fit, draw a line through the center of the most points. This line will have as its y-intercept a value around 12 and a gentle slope. This means the answer choice is C.
