the wolf population in a local wildlife area is currently 12. due to a new conservation effort, conservationists hope the wolf p
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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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The formula of a volume of a cuboid:
l - length
w - width
h - height
We have:
l = (x + 4) cm
w = (x + 1) cm
h = 3 cm
Substitute:
<em>use distributive property</em>
<em>combine like terms</em>