Online Course Discussion Forum
Math Challenge I-C Handout 5
Could someone help me with these problems? Specifically, I don't understand the question for 5.15 and I don't know how to do 5.28 and 5.30.
Question 5.15:
The domain of the parabola y+3=−2(x−4)2y+3=−2(x−4)2 is all yy such that y≤Ly≤L for some integer LL. What is LL?
Question 5.28:
Rewrite each of the following functions in the form y=axy=ax for a rational number a>0
Part a): y=122xy=122x.
Part b): y=2−2x
Question 5.30:
Nickel-63 has a half-life of about 11 century. This means that after every century, half of the nickel-63 you have will decay. Suppose you start out with 22 kg of nickel-63. Write an equation that gives the amount (in kg) of nickel remaining after xxcenturies.
y=ThanksQuestion 5.15 should be the "range" not the domain. This is now fixed. Thanks for the heads up!
Hint for 5.28: The key here is going to be using our rules of exponents to combine the numbers. So for part a), we want to first write $\displaystyle \frac{1}{2}$ as $2^\text{something}$ and then combine it with the $2^x$. For part b), take a look at the rules of exponents again. Which rule allows us to say, for example, $(2^3)^4 = 2^{3\times 4} = 2^{12}$?
Hint for 5.30: Start by making a table answering how much nickel-63 is left after $0$ centuries, after $1$ century, after $2$ centuries, etc. To get started we have $2$ kg after $0$ years and $\frac{1}{2}\times 2 = 1$ kg after $1$ century. Can you find a pattern and then turn this pattern into a formula?
Question 5.28:
Part b): y=2−2x
y=(2^x)^-2
Thank you! Is this what you mean? I feel like part b is already simplified to that form and my answer is not exactly writing in that form.
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