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

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

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

that is all.
and

means that the logarithm itself delivered -1.
and 8^-1 = 1/8
so, p(t) = 1 for t = 1/8
Answer:
total - given, 360 -139 = 221
Answer:
a) (0, ∞)
b) (-∞, ∞)
c) x = 0
Step-by-step explanation:
It helps to have some idea what the log function is.
__
a) The domain is all positive numbers: (0, ∞).
b) The range is all real numbers: (-∞, ∞). (The vertical translation downward by 5 units does not change that.)
c) There is a vertical asymptote where the argument of the log function is zero: at x=0.
Answer:
Taking P(x) = x³-12x-16 as an example
Step-by-step explanation:
For a polynomial, if
x = a is a zero of the function, then (x − a) is a factor of the function.
We have two unique zeros:
−2 and 4. However, −2 has a multiplicity of 2, which means that the factor that correlates to a zero of −2 is represented in the polynomial twice.
Following how it's constructed
zero at -2, multiplicity 2
zero at 4, multiplicity 1
p(x)=x−(−2))²(x−4)¹
Thus,p(x)=(x+2)²(x−4)
Expand: p(x)=(x²+4x+4)(x−4)
p(x) =x³−12x−16