Consider the functions f(x) = 5x – 2, g(x) = 5x² + 2 and r(x) = –2x + 4.
2 answers:
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The perimeter of the square patio is the sum of its side lengths
The length of the patio is: 8x + 2
The given parameters are:
The perimeter of a square is:
So, we have:
Divide both sides by 4
Hence, the length of the patio is: 8x + 2
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Considering the function for the remaining amount of cesium in the atmosphere, F(x) = 1000×0.5^(x/30), we have;
First part:
- The area will be safe again in about 100 years time.
Second part;
- The y-intercept is at the start of the measurement
Third part;
- The function is a decay function
First part;
The given function for the remaining amount of cesium is presented as follows;
When 100 kg. of cesium is remaining, we have;
Which gives;
- Therefore, the area will be safe again in approximately 100 years.
Second part;
The y-intercept is given by the point where <em>x </em>= 0
At the y-intercept, we therefore have;
- F(0) = 1000
At the y-intercept, the amount of cesium remaining, F(x) is 1,000, which is the initial amount of cesium.
- The y-intercept is therefore, at the start of the measurement, where 1000 kg. is present in the atmosphere.
Third part;
The amount of cesium remaining F (x) decreases as the time, <em>x</em>, increases, the function is therefore a decay function.
Learn more about exponential functions here;
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