Mila borrowed some money from her friend in order to buy a new video game system and agreed to pay the friend back a constant amount each week. mila originally borrowed $100 from her friend and after 3 weeks, she still owed her friend $70. write an equation for the function l(t), representing the amount mila owes her friend after t weeks.

L(t) = 100 - 10t

Step-by-step explanation:

The total amount of money that Mila borrowed from her friend in order to buy the video game system is $100. Let x represent the constant amount that she agreed to pay each week.

After 3 weeks, she still owed her friend $70. This means that the amount that she paid in 3 weeks is 100 - 70 = $30. Since she pays $x per week, her payment in 3 weeks will be 3×x = $3x. Therefore,

3x = 30

x = 30/3 = 10

She pays $10 each week

Let t represent the number of weeks. The function, L(t), representing the amount Mila owes her friend after t weeks would be

L(t) = 100 - 10t

a) 40 more; b) old factory:   10%, new factory:   16%; c) week 4

explanation:

a) at week 0, we see in the graph that the new factory produces 190 specialty items.  

using the function, substituting 0 in for w,

this is a difference of 230-190 = 40.

b) the function for the old factory is written in the form f(x) = a(1+r)ˣ, where a is the original amount, x is the amount of time and r is the growth rate.   the equation for the old factory is ; 230 is in place of a and is the original amount; w is the amount of time; which means 1+r = 1.1.   this means that r must be 0.1 or 10%.

for the new factory, we find the percent of increase to find the growth rate; the formula for this is

between the first two points, the amount of change is 220-190 = 30; this gives us

30/190 = 0.158 ≈ 0.16 = 16%

c) at week 0, the old factory has 230 while the new factory has 190.

at week 1, the old factory has 230(1.1) = 253 while the new factory has 220.

at week 2, the old factory has 230(1.1²) = 278.3 while the new factory has 252.

at week 3, the old factory has 230(1.1³) = 306.13 while the new factory has 290.

at week 4, the old factory has 230(1.1⁴) = 336.743 while the new factory has 337.   this is the first week that the new factory surpasses the old.