Answer:
y
=
4
(
1
2
)
x
Explanation:
An exponential function is in the general form
y
=
a
(
b
)
x
We know the points
(
−
1
,
8
)
and
(
1
,
2
)
, so the following are true:
8
=
a
(
b
−
1
)
=
a
b
2
=
a
(
b
1
)
=
a
b
Multiply both sides of the first equation by
b
to find that
8
b
=
a
Plug this into the second equation and solve for
b
:
2
=
(
8
b
)
b
2
=
8
b
2
b
2
=
1
4
b
=
±
1
2
Two equations seem to be possible here. Plug both values of
b
into the either equation to find
a
. I'll use the second equation for simpler algebra.
If
b
=
1
2
:
2
=
a
(
1
2
)
a
=
4
Giving us the equation:
y
=
4
(
1
2
)
x
If
b
=
−
1
2
:
2
=
a
(
−
1
2
)
a
=
−
4
Giving us the equation:
y
=
−
4
(
−
1
2
)
x
However! In an exponential function,
b
>
0
, otherwise many issues arise when trying to graph the function.
The only valid function is
y
=
4
(
1
2
)
x
This is pretty simple. All you have to do is make the first and second fraction share a denominator by multiplying them by each other.
6 <span>• 9 = 54
Then multiply each numerator by the opposing denominator.
1 </span><span>• 9 = 9
2 </span><span>• 6 = 12
Here are the new fractions:
9/54
12/54
Now add the 9 and 12 together.
9 + 12 = 21
The complete fraction:
21/54
Subtract 21 from 54 so you can get the remainder of the sweater.
54 - 21 = 33
This is the remainder fraction:
33/54
Can you simplify this? Yes, of course! They can both be divided by 3!
11/18
That is the remainder of the sweater. But you still have to divide it in half! After all, Linda only knitted half of the remaining sweater. Dividing it in half can be done just by multiplying the denominator by 2.
11/36
That should be your answer! Apologies if I got something wrong.</span>
You need to type the same equation that’s shown above of the text box. If there’s still a technical issue, let me know, and I’ll try to help!
Answer:
Here's a screenshot. Hope this helps
