The amount of the radioactive material in the vault after 140 years is 210 pounds
<h3>How to determine the amount</h3>
We have that the function is given as a model;
f(x) = 300(0.5)x/100
Where
- x = number of years of the vault = 140 years
- f(x) is the amount in pounds
Let's substitute the value of 'x' in the model
f(x) = 300(0.5)x/100


f(140) = 210 pounds
This mean that the function of 149 years would give an amount of 210 pounds rounded up to the nearest whole number.
Thus, the amount of the radioactive material in the vault after 140 years is 210 pounds
Learn more amount radioactive decay here:
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At a certain time of day, a 5.5 foot tall man has a 6 foot shadow. if a tree is 19.25 feet tall, what is the length of the shadow of the tree(x=shadow of the tree)
the equation for the problem is...
5.5/6=19.25/x
you then multiply the denominators on both sides...
5.5x=19.25*6
you then solve on one side...
5.5x=115.5
and then divide 5.5 on both sides to leave x alone...
x=21
the shadow of the tree is 21
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Answer:
Quadrant IV
Step-by-step explanation:
15π/4 is the same angle as 15π/4 − 2π = 7π/4. Which terminates in the fourth quadrant.
i. Domain and Range
The given function is

The domain of this function is,



The range refers to the y-values for which x is defined. x is defined for all values of y.
The range is all real numbers. See graph
ii. x-and-y-intercept
For x- intercept intercept we put 
This implies that;

This will give us







The x-intercepts are 
For y-intercept, we put
to obtain;


The y-intercept is

iii. Horizontal asyptote
Since degree of the numerator and the denominator are the same, there is a horizontal asymptote
To find the horizontal asymptote.
We divide the leading coefficient of the numerator by the leading coefficient of the denominator.
The horizontal asymptote is 
iv. Vertical asymptote
To find the vertical asymptote, we equate the denominator to zero to get;

This implies that;

Split the middle term

Factor

Factor further


The vertical asymptotes are 