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 [tex]y=mx+b[/tex]
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: [tex]y=8x+b[/tex]
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:
[tex]49=8(3)+b[/tex]
49=24+b
b=49-24=25.
a) The fee is $25
b) We now write the equation in full to get: [tex]y=8x+25[/tex]
To find the cost for 5 hours we put x=5 into this equation and solve for y.
[tex]y=8(5)+25[/tex]
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:
[tex]198,000=-12,000(4)+b[/tex]
[tex]198,000=-48,000+b[/tex]
[tex]b=198,000+48,000=246,000[/tex]
Hence he started with 246,000 customers
b) The equation now becomes [tex]y=-12,000x+246,000[/tex]
To find how many years he will have 6000 followers, we substitute y=6000 and solve for x.
[tex]6000=-12,000x+246,000[/tex]
[tex]6000-246,000=-12,000x[/tex]
[tex]-240,000=-12,000x[/tex]
[tex]x=\frac{240,000}{12,000}[/tex]
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.
[tex]73=0.25(32)+b[/tex]
[tex]73=8+b[/tex]
[tex]b=73-8[/tex]
[tex]b=65[/tex]
Hence the one-time fee is $65
b) The equation now becomes:
[tex]y=0.25x+65[/tex]
To find how much it will cost to drive 81 miles, we substitute x=81 and solve for y.
[tex]y=0.25*81+65[/tex]
[tex]y=20.25+65[/tex]
[tex]y=85.25[/tex]
The cost for 81 miles is $85.25
