Answer:
p(t) = 0 for t = 1
p(t) = 1 for t = 1/8 = 8^-1
Step-by-step explanation:
the graph you will have to do yourself.
just go there and type in
[tex] - log_{8}(x) [/tex]
well, don't type "log" in letters.
you start by typing the "-" sign, and then you need to look up the functions by clicking on the "funcs" button and look for the log functions .
pick the
[tex] log_{a}[/tex]
option. and then simply enter 8 as the first parameter in the {} brackets and x as the second in the () brackets.
and then you see.
any logarithm is 0 for x (or t) = 1.
because any a⁰ = 1.
and the logarithm gives you that exponent of the base number that leads to the given x value.
in other words : a logarithm is the inverse function of an exponential function.
the exponential function is
y = a^x
and the logarithm then determines
[tex]x = log_{a}(y) [/tex]
that is all.
and
[tex] - log_{8}(x) = 1[/tex]
means that the logarithm itself delivered -1.
and 8^-1 = 1/8
so, p(t) = 1 for t = 1/8
