Answer:
![y=8 \cdot (\frac{5}{4})^x](https://tex.z-dn.net/?f=y%3D8%20%5Ccdot%20%28%5Cfrac%7B5%7D%7B4%7D%29%5Ex)
![f(x)=8 \cdot (\frac{5}{4})^x](https://tex.z-dn.net/?f=f%28x%29%3D8%20%5Ccdot%20%28%5Cfrac%7B5%7D%7B4%7D%29%5Ex)
or
![f(x)=8 \cdot (1.25)^x](https://tex.z-dn.net/?f=f%28x%29%3D8%20%5Ccdot%20%281.25%29%5Ex)
Step-by-step explanation:
We are going to see if the exponential curve is of the form:
, (
).
If you are given the
intercept, then
is easy to find.
It is just the
coordinate of the
intercept is your value for
.
(Why? The
intercept happens when
. Replacing
with 0 gives
. This says when
.)
So
.
So our function so far looks like this:
![y=8 \cdot b^x](https://tex.z-dn.net/?f=y%3D8%20%5Ccdot%20b%5Ex)
Now to find
we need another point. We have two more points. So we will find
using one of them and verify for our resulting equation works for the other.
Let's do this.
We are given
is a point on our curve.
So when
,
.
![10=8 \cdot b^1](https://tex.z-dn.net/?f=10%3D8%20%5Ccdot%20b%5E1)
![10=8 \cdot b](https://tex.z-dn.net/?f=10%3D8%20%5Ccdot%20b)
Divide both sides by 8:
![\frac{10}{8}=b](https://tex.z-dn.net/?f=%5Cfrac%7B10%7D%7B8%7D%3Db)
Reduce the fraction:
![\frac{5}{4}=b](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B4%7D%3Db)
So the equation if it works out for the other point given is:
![y=8 \cdot (\frac{5}{4})^x](https://tex.z-dn.net/?f=y%3D8%20%5Ccdot%20%28%5Cfrac%7B5%7D%7B4%7D%29%5Ex)
Let's try it. So the last point given that we need to satisfy is
.
This says when
,
.
Let's replace
with 2 and see what we get for
:
![y=8 \cdot (\frac{5}{4})^2](https://tex.z-dn.net/?f=y%3D8%20%5Ccdot%20%28%5Cfrac%7B5%7D%7B4%7D%29%5E2)
![y=8 \cdot \frac{25}{16}](https://tex.z-dn.net/?f=y%3D8%20%5Ccdot%20%5Cfrac%7B25%7D%7B16%7D)
![y=\frac{8}{16} \cdot 25](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B8%7D%7B16%7D%20%5Ccdot%2025)
![y=\frac{1}{2} \cdot 25}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B1%7D%7B2%7D%20%5Ccdot%2025%7D)
![y=\frac{25}{2}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B25%7D%7B2%7D)
![y=12.5](https://tex.z-dn.net/?f=y%3D12.5)
So we are good. We have found an equation satisfying all 3 points given.
The equation is
.
Answer:
4:7
hope this helps :) plz brainliest if helps
Step-by-step explanation:
Hi
6% increase is multiply by 1,06
done 40 times
so : 250* 1,06^40 = 2571 ,
Answer:x=-1
Step-by-step explanation:
Answer:
2 lbs. for $4.50
Step-by-step explanation:
Do a ratio
2 : 4.50
You want to see how much it cost per pound, so divide them by 2
2 ÷ 2 : 4.50 ÷ 2
1 : 2.25
So per pound, the hamburger will cost $ 2.25
________________________________________________________
3 : 6.90
You want to see how much it cost per pound, so all you need to do is divide them by 3
3 ÷ 3 : 6.90 ÷ 3
1 : 2.3
So for the first one, it cost 2.25 per pound, and for the second one, it cost 2.3 per pound....the one that is better will be 2.25 because it cost 5 cents less than the second one
Hope this helped!
Have a supercalifragilisticexpialidocious day!