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1 answer:
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Answer:
a) f(x) tends to minus infinity
b) (0,768) is the y-intercept, (4,0) and (-3,0) are the x-intercepts.
Step-by-step explanation:
Our function is a polynomial of degree 4.
a) The monomial with highest degree determines the behavior of f(x) when x tends to infinity and when x tends to -infinity. This monomial is -4x⁴. Without expanding completely, (x-4)³ has x³ as a summand, which multiplies with -4x from the first factor, to give -4x⁴. When x goes to infinity (or minus infinitive), x²=(x²)² is positive (nonzero squares are always positive) thus -4x² is negative, and f(x) tends to minus infinity.
b). To find the y-intercept, we compute (0,f(0)). Since f(0)=-4(3)(-4)³=768, then (0,768) is the point of the y-intercept.
For the x-intercept, solve f(x)=0. f(x)=0 has the solutions x=-3 and x=4. In this case, the x-intercept is in both x=0 and x=4. Then (-3,0) and (4,0) are x-intercepts.
Using an exponential function, it is found that the bottle contains 255,960 atoms of tritium after 11 years.
<h3>What is an exponential function?</h3>A decaying exponential function is modeled by:
In which:
- A(0) is the initial value.
- r is the decay rate, as a decimal.
In this problem:
- The bottle initially contained 450,000 tritium atoms, hence A(0) = 450000.
- The amount decays by about 5% per year, hence r = 0.05.
Thus, the equation is given by:
After 11 years, the amount is given by:
The bottle contains 255,960 atoms of tritium after 11 years.
More can be learned about exponential functions at brainly.com/question/25537936