Question

Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 4^-x and y = 2^(x + 3) intersect are the solutions of the equation 4^-x = 2^(x + 3).

Part B: Make tables to find the solution to 4^-x = 2^(x + 3). Take the integer values of x between -3 and 3.

Part C: How can you solve the equation 4^-x = 2^(x + 3) graphically?

Answer 1

for part A, the points on the graph of both are \((x,y)\) and in once case it is \((x, 4^{-x})\) and in the other it is \((x,2^{x+3})\)
where they intersect both the \(x\) and the \(y\) values will be the same, so \(4^{-x}\) will be equal to \(2^{x+3}\) at that point

Answer 2

Thanks :). Can you help me with part 2? I don't know how to make the tables.

Answer 3

it means pick \(x\) as the first number and compute \(y\) for the second
for example, if \(x=-3\) then \(y=4^{-x}=4^{-(-3)}=4^3=64\) and
\[2^{x+3}=2^{2+3}=2^5=32\]

Answer 4

actually i made a mistake there
if \(x=-3\) then
\[2^{x+2}=2^{-3+2}=2^{-1}=\frac{1}{2}\]

Answer 5

damn another mistake, it is \(2^{x+3}\) not \(2^{x+2}\) scratch that
\[2^{-3-3}=2^0=1\]

Answer 6

Wait, so would the tables look like this?:

Table for y = 4^-x:
x y
-3 64
-2 16
-1 4
0 1
1 0.25
2 0.0625
3 0.015625

Table for y = 2^(x+3):
x y
-3 1
-2 2
-1 3
0 8
1 16
2 32
3 64

Answer 7

@satellite73 ?

Answer 8

Wait sorry like this:

Table for y = 4^-x:
x y
-3 64
-2 16
-1 4
0 1
1 0.25
2 0.0625
3 0.015625

Table for y = 2^(x+3):
x y
-3 1
-2 2
-1 4
0 8
1 16
2 32
3 64

Answer 9

@wio @shamim ? are you guys there? could you please help me?