Answer:
Part a) The equation in point slope form is [tex]y-11.2=-0.025(x-37)[/tex]
Part b) [tex]6.1\ in[/tex]
Step-by-step explanation:
Part a) Determine the equation of the line in point slope form
Let
x -----> the time in minutes
y -----> the height of the candle in inches
we know that
After 37 minutes, the candle was 11.2 inches tall
so
we have the point
(37,11.2)
Eighteen minutes later, it was 10.75 inches tall
so
we have the point
(37+18,10.75) -----> (55,10.75)
Find the slope of the linear equation
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute the values
[tex]m=\frac{10.75-11.2}{55-37}[/tex]
[tex]m=\frac{-0.45}{18}[/tex]
[tex]m=-0.025\frac{in}{min}[/tex] ----> is negative because is a decreasing function
The equation of the line in point slope form is equal to
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=-0.025[/tex]
[tex](x1,y1)=(37,11.2)[/tex]
substitute
[tex]y-11.2=-0.025(x-37)[/tex]
Part b) Determine the height of the candle after 4 hours
Remember that
[tex]1\ h=60\ min[/tex]
so
[tex]4\ h=4(60)=240\ min[/tex]
For x=240 min
substitute in the linear equation
[tex]y-11.2=-0.025(240-37)[/tex]
[tex]y-11.2=-5.075[/tex]
[tex]y=-5.075+11.2[/tex]
[tex]y=6.125\ in[/tex]
Round to the tenth place
[tex]y=6.1\ in[/tex]
