Both problems give you a function in the second column and the x-values. To find out the values of a through f, you need to plug in those x-values into the function and simplify!
You need to know three exponent rules to simplify these expressions:
1) The negative exponent rule says that when a
base has a negative exponent, flip the base onto the other side of the
fraction to make it into a positive exponent. For example, [tex] 3^{-2} =
\frac{1}{3^{2} } [/tex].
2) Raising a fraction to a power is the same as separately raising the numerator and denominator to that power. For example, [tex](\frac{3}{4}) ^{3} = \frac{ 3^{3} }{4^{3} } [/tex].
3) The zero exponent rule says that any number
raised to zero is 1. For example, [tex] 3^{0} = 1[/tex].
Back to the Problem:
Problem 1
The x-values are in the left column. The title of the right column tells you that the function is [tex]y = 4^{-x}[/tex]. The x-values are:
1) x = 0
Plug this into [tex]y = 4^{-x}[/tex] to find letter a:
[tex]y = 4^{-x}\\
y = 4^{-0}\\
y = 4^{0}\\
y = 1[/tex]
2) x = 2
Plug this into [tex]y = 4^{-x}[/tex] to find letter b:
[tex]y = 4^{-x}\\
y = 4^{-2}\\
y = \frac{1}{4^{2}} \\
y= \frac{1}{16} [/tex]
3) x = 4
Plug this into [tex]y = 4^{-x}[/tex] to find letter c:
[tex]y = 4^{-x}\\
y = 4^{-4}\\
y = \frac{1}{4^{4}} \\
y= \frac{1}{256} [/tex]
Problem 2
The x-values are in the left column. The title of the right column tells you that the function is [tex]y = (\frac{2}{3})^x[/tex]. The x-values are:
1) x = 0
Plug this into [tex]y = (\frac{2}{3})^x[/tex] to find letter d:
[tex]y = (\frac{2}{3})^x\\
y = (\frac{2}{3})^0\\
y = 1[/tex]
2) x = 2
Plug this into [tex]y = (\frac{2}{3})^x[/tex] to find letter e:
[tex]y = (\frac{2}{3})^x\\ y = (\frac{2}{3})^2\\ y = \frac{2^2}{3^2}\\
y = \frac{4}{9} [/tex]
3) x = 4
Plug this into [tex]y = (\frac{2}{3})^x[/tex] to find letter f:
[tex]y = (\frac{2}{3})^x\\ y = (\frac{2}{3})^4\\ y = \frac{2^4}{3^4}\\ y = \frac{16}{81}[/tex]
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Answers:
a = 1
b = [tex]\frac{1}{16}[/tex]
c = [tex] \frac{1}{256} [/tex]
d = 1
e = [tex]\frac{4}{9} [/tex]
f = [tex]\frac{16}{81}[/tex]
