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Question 1149850: Chloe borrowed some money from her friend in order to help buy a new video game system and agreed to pay the friend back a constant amount each week. Chloe originally borrowed $40 from her friend and after 6 weeks, she still owed her friend $16. Write an equation for the function L(t), representing the amount Chloe owes her friend after t weeks.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
Chloe borrowed $40. After 6 weeks, Chloe still owes $16. This means she paid back 40-16 = 24 dollars so far. Divide those 24 dollars over the 6 weeks
24/6 = 4
Chloe pays her friend back at a rate of 4 dollars per week. This helps find the slope, which is the rate of change or speed. Specifically we use the negative version of this number to indicate the balance is going down. Let m = -4 be that slope. The starting amount is b = 40
We go from y = mx+b to y = -4x + 40. Let's see what happens when we plug x = 6 into the equation
y = -4x+40
y = -4*6+40
y = 16
we get the proper value of 16, indicating after x = 6 weeks, Chloe still owes y = 16 dollars.
Replace x with t. Replace y with L(t). Doing those two things leads to this final answer
L(t) = -4t + 40
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