Remark
The basic equation is y = mx + b
y = the total amount of money
m = The amount of money he save each month (it is a constant).
b = the y intercept which is his starting amount or 120 dollars.
x = the number of months (this is a variable).
After 3 months he has 840 dollars. That's y
840 = 3*m + 120 Subtract 120 from both sides
840 - 120 = 3m
720 = 3m
240 = m So he saves 240 every month.
Now the equation becomes.
y = 240 * x + 120
Savings after 24 months
y = Total
m = 240 dollars/month
x = 24 months
b = 120
y = 24*240 + 120
y = 5760 + 120
y = 5580
He had 5580 dollars after saving for 2 years (or 24 months total) This assumes that when he started, he took his birthday money and added a 1 month payment to it
<span>N(t) = 16t ; Distance north of spot at time t for the liner.
W(t) = 14(t-1); Distance west of spot at time t for the tanker.
d(t) = sqrt(N(t)^2 + W(t)^2) ; Distance between both ships at time t.
Let's create a function to express the distance north of the spot that the luxury liner is at time t. We will use the value t as representing "the number of hours since 2 p.m." Since the liner was there at exactly 2 p.m. and is traveling 16 kph, the function is
N(t) = 16t
Now let's create the same function for how far west the tanker is from the spot. Since the tanker was there at 3 p.m. (t = 1 by the definition above), the function is slightly more complicated, and is
W(t) = 14(t-1)
The distance between the 2 ships is easy. Just use the pythagorean theorem. So
d(t) = sqrt(N(t)^2 + W(t)^2)
If you want the function for d() to be expanded, just substitute the other functions, so
d(t) = sqrt((16t)^2 + (14(t-1))^2)
d(t) = sqrt(256t^2 + (14t-14)^2)
d(t) = sqrt(256t^2 + (196t^2 - 392t + 196) )
d(t) = sqrt(452t^2 - 392t + 196)</span>
