The answer is nonlinear. It goes in a sharp downward curve, whereas a linear function is a straight line.
To simplify the function, we need to know some basic identities involving exponents.
1. b^(ax)=(b^x)^a=(b^a)^x
2. b^(x/d) = (b^x)^(1/d) = ((b^(1/d)^x)
Now simplify f(x), where
f(x)=(1/3)*(81)^(3*x/4)
=(1/3)(3^4)^(3*x/4) [ 81=3^4 ]
=(1/3)(3^(4*3*x/4) [ rule 1 above ]
=(1/3) (3^(3*x)
=(1/3)(3^(3x)) [ or (1/3)(27^x), by rule 1 ]
(A) Initial value is the value of the function when x=0, i.e.
initial value
= f(0)
=(1/3)(3^(3x))
=(1/3)(3^(3*0))
=(1/3)(3^0)
=(1/3)(1)
=1/3
(B) the simplified base base is 3 (or 27 if the other form is used)
(C) The domain for an exponential function is all real values ( - ∞ , + ∞ ).
(D) The range of an exponential function with a positive coefficient and without vertical shift is ( 0, + ∞ ).
(x-h)²+(y-k)²=r² is the equation of a circle with radius of r
so if x-h=4 and y-k=3 then
4²+3²=r²
16+9=r²
25=r²
sqrt both sides
5=r
radius is 5 units
It's simple how many cups are in a pint.....4 if I remember correctly...its been awhile.....so you have 16 cups total so you divide that by the price....so it should be $1.024375 rounded to the nearest cent which is $1.02.......hope that helps
