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Answer:
The rate of change of f(x) is greater than that of g(x)
They have the same y intercept of 14
Step-by-step explanation:
Given
Table for function f(x)
Required
Compare their rate of change and intercept
For g(x), we have:
The form of an equation is:
Where
So:
For f(x): Start by calculating the slope (m)
The intercept is calculated using:
Where
--- we want to solve for y
So:
Multiply both sides by 2
Make y the subject
So, we have:
and
-- for g(x)
and
--- for f(x)
By comparison:
The rate of change (i.e. slope) of f(x) is greater than that of g(x) because
They have the same y intercept of 14
Answer:
Approximately 3 grams left.
Step-by-step explanation:
We will utilize the standard form of an exponential function, given by:
In the case of half-life, our rate <em>r</em> will be 1/2. This is because 1/2 or 50% will be left after <em>t </em>half-lives.
Our initial amount <em>a </em>is 185 grams.
So, by substitution, we have:
Where <em>f(t)</em> denotes the amount of grams left after <em>t</em> half-lives.
We want to find the amount left after 6 half-lives. Therefore, <em>t </em>= 6. Then using our function, we acquire:
Evaluate:
So, after six half-lives, there will be approximately 3 grams left.