Question 1168699: If f(x)=7^x , then f(x+3)-f(x+1) equals:
A) 2f(x)
B) 336f(x)
C) 342f(x)
D) 343
E) 2
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! f(x) = 7^x
f(x+3) = 7^(x+3)
f(x+1) = 7^(x+1)
f(x+3) - f(x+1) = 7^(x+3) - 7^(x+1)
f(x+3) = 7^(x+3) = 7^3 * 7^x
f(x+1) = 7^(x+1) = 7^1 * 7^x
f(x+3) - f(x+1) = 7^3 * 7^x - 7^1 * 7^x
factor out 7^x to get:
f(x+3) - f(x+1) = (7^3 - 7^1) * 7^x
this becomes f(x+3) - f(x+1) = 336 * 7^x
since 7^x = f(x), you get f(x+3) - f(x+1) = 336 * f(x).
that would be selection B.
what it says is that f(x+3) - f(x+1) is equivalent to 336 * f(x).
these two expressions can be made equal to y and graphed to show that they make identical graphs.
your two equations to graph are:
y = 7^(x+3) - 7^(x+1) and y = 336*7^x
you will see that, on the graph, these these two equations make the same graph. in other words, the graphs are identical because the equations are equivalent.
here's the graph.
the graph of each equation is in red.
you only see one curve, because the graphs are identical.
if you were to calculate both equations for x = 0 to 5, you would get:
x y = 336*7^x y=7^(x+3) - 7^(x+1)
0 336*7^0 = 336 7^3 - 7^1 = 336
1 336*7^1 = 2,352 7^4 - 7^2 = 2,352
2 336*7^2 = 16,464 7^5 - 7^3 = 16,464
3 336*7^3 = 115,248 7^6 - 7^4 = 115,248
4 336*7^4 = 806,736 7^7 - 7^5 = 806,736
5 336*7^5 = 5,647,152 7^8 - 7^6 = 5,647,152
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