Answer:
x=0,-7
Step-by-step explanation:
They are called equations
The complete question is
<span>-2 2/3, -5 1/3, -10 2/3, -21 1/3, -42 2/3, ... Which formula can be used to describe the sequence?
a. f(x + 1) = –2f(x)
b. f(x + 1) = f(x)
c. f(x + 1) = -f(x)
d. f(x + 1) = 2f(x)
case a) </span>f(x + 1) = –2f(x)
for f(x)=-2 2/3
f(x+1)=-2*[-2 2/3]=5 1/3
5 1/3 is not -5 1/3
therefore
this is not the formula
case b) f(x + 1) = f(x)
for f(x)=-2 2/3
f(x+1)=-2 2/3
-2 2/3 is not -5 1/3
therefore
this is not the formula
case c) f(x + 1) = -f(x)
for f(x)=-2 2/3
f(x+1)=2 2/3
2 2/3 is not -5 1/3
therefore
this is not the formula
case d) f(x + 1) =2f(x)
for f(x)=-2 2/3
f(x+1)=2*[-2 2/3]=-5 1/3
for f(x)=-5 1/3
f(x+1)=2*[-5 1/3]=-10 2/3
for f(x)=-10 2/3
f(x+1)=2*[-10 2/3]=-21 1/3
for f(x)=-21 1/3
f(x+1)=2*[-21 1/3]=-42 2/3
therefore
the answer is the option
d. f(x + 1) = 2f(x)
When it says f(x) and x is replaced with a number, it just means replace the x in the equation with that number.
(Simpler) Way to solve using the graph:
Go to where x = -4 (4 spaces right of the center) and look above and below it for the line. Wherever the line is, is the answer. So f(-4) = 2 because when x is -4, the y value is 2.
Example of solving with an equation:
f(3) = 2
f(3) = 2(3)
f(3) = 6
You create an equation for the line, than substitute -4 in to the equation.
<span>This is decay. The exponent has a negative sign. The reciprocal of 2 is 0.5. So N(t) can be rewritten as 0.5^(t/8). The base is fraction less than 1, which is decay.</span>
