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, + ∞ ).
Equation of a line is given by y - y1 = m(x - x1); where m is the slope.
y - 4 = 2/5 (x - (-2))
y - 4 = 2/5 (x + 2)
Hope this helps! :)
Answer:
I used Desmos. Heres a picture of what its supposed to look like.
Step-by-step explanation:
11. x² - 7x = 0
x(x) - x(7) = 0
x(x - 7) = 0
x = 0 or x - 7 = 0
+ 7 + 7
x = 7
Solution Set: {0, 7}
12. 3x² - 4x = 20x + 27
+ 4x + 4x
3x² = 24x + 27
3x² - 24x - 27 = 0
x = -(-24) ± √((-24)² - 4(3)(-27))
2(3)
x = 24 ± √(576 + 324)
6
x = 24 ± √(900)
6
x = 24 ± 30
6
x = 4 ± 5
x = 4 + 5 or x = 4 - 5
x = 9 or x = -1
Solution Set: {9, -1}
Answer:
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Step-by-step explanation:
