Answer:
1. a) $ 25
b) $65
2) a) 246,000 followers
b) In 20 years
3a) $65
b) $85.25
Step-by-step explanation:
1. A linear equation is modeled by ![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
where b is the one time fee you pay and m=$8 is how much you pay per hour.
y is the total cost and x is the number of hours.
Hence the equation becomes: ![y=8x+b](https://tex.z-dn.net/?f=y%3D8x%2Bb)
Since Jill rented for 3 hours and paid $49, x=3 and y=49.
We substitute and solve for the one-time fee, b.
This implies that:
![49=8(3)+b](https://tex.z-dn.net/?f=49%3D8%283%29%2Bb)
49=24+b
b=49-24=25.
a) The fee is $25
b) We now write the equation in full to get: ![y=8x+25](https://tex.z-dn.net/?f=y%3D8x%2B25)
To find the cost for 5 hours we put x=5 into this equation and solve for y.
![y=8(5)+25](https://tex.z-dn.net/?f=y%3D8%285%29%2B25)
y=40+25=$65
2a) We still use the equation y=mx+b.
b is the number of followers he started with.
This time m=-12,000 because he is losing followers at the rate of 12,000
The equation becomes: y=-12,000x+b
After 4 years he was down to 198,000.
This implies that, when x=4,y=198,000
We substitute to get:
![198,000=-12,000(4)+b](https://tex.z-dn.net/?f=198%2C000%3D-12%2C000%284%29%2Bb)
![198,000=-48,000+b](https://tex.z-dn.net/?f=198%2C000%3D-48%2C000%2Bb)
![b=198,000+48,000=246,000](https://tex.z-dn.net/?f=b%3D198%2C000%2B48%2C000%3D246%2C000)
Hence he started with 246,000 customers
b) The equation now becomes ![y=-12,000x+246,000](https://tex.z-dn.net/?f=y%3D-12%2C000x%2B246%2C000)
To find how many years he will have 6000 followers, we substitute y=6000 and solve for x.
![6000=-12,000x+246,000](https://tex.z-dn.net/?f=6000%3D-12%2C000x%2B246%2C000)
![6000-246,000=-12,000x](https://tex.z-dn.net/?f=6000-246%2C000%3D-12%2C000x)
![-240,000=-12,000x](https://tex.z-dn.net/?f=-240%2C000%3D-12%2C000x)
![x=\frac{240,000}{12,000}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B240%2C000%7D%7B12%2C000%7D)
x=20.
3. We still use the equation: y=mx+b.
This time m=0.25 is the rate per mile.
This implies y=0.25x+b
Since Kyle drove 32 miles and spent $73, we have y=73 when x=32
We substitute these values and solve for x.
![73=0.25(32)+b](https://tex.z-dn.net/?f=73%3D0.25%2832%29%2Bb)
![73=8+b](https://tex.z-dn.net/?f=73%3D8%2Bb)
![b=73-8](https://tex.z-dn.net/?f=b%3D73-8)
![b=65](https://tex.z-dn.net/?f=b%3D65)
Hence the one-time fee is $65
b) The equation now becomes:
![y=0.25x+65](https://tex.z-dn.net/?f=y%3D0.25x%2B65)
To find how much it will cost to drive 81 miles, we substitute x=81 and solve for y.
![y=0.25*81+65](https://tex.z-dn.net/?f=y%3D0.25%2A81%2B65)
![y=20.25+65](https://tex.z-dn.net/?f=y%3D20.25%2B65)
![y=85.25](https://tex.z-dn.net/?f=y%3D85.25)
The cost for 81 miles is $85.25