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, + ∞ ).
answer : 10 fish in each tank because 10 time 5 equals 50 and there 5 tanks sotaht mean 50 divided by 5 it will be 10 fish
The mean is 23 because it is the middle number
The temperature at the beginning of the day was 6.2°F
Let x represent the temperature at the beginning of the day.
Since, the temperature of a city doubles during the day, and then decreases by 14.1ºF after the sun goes down, hence:
Temperature at end of day = 2x - 14.1
Also, the temperature at the end of the day is −1.7°F, hence:
2x - 14.1 = -1.7
2x = 12.4
x = 6.2°F
The temperature at the beginning of the day was 6.2°F
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